Revelation 3:10 is rightly know as a passage that supports the pre-trib rapture doctrine, but the second half of the verse introduces us to the first use of the term "earth dwellers." "Because you have kept the word of My perseverance, I also will keep you from the hour of testing, that hour which is about to come upon the whole world, to test those who dwell upon the earth." 3:10 is the first use in Revelation of a phrase I call "earth dwellers" but usually translated "those who dwell upon the earth." This phrase is used eleven times in nine verses in Revelation (3:10; 6:10; 8:13; 11:10 2xs; 13:8, 12, 14 2xs; 14:6; 17:8). "Earth dwellers" is a designation for persistent unbelievers during the tribulation.
Old Testament Background
Like most New Testament terminology, "earth dwellers" originates in the Old Testament. A couple forms of the construct is used almost 50 times in the Hebrew Old Testament,  not including a similar phrase "world dwellers" that occurs five times.  The overwhelming majority of times that "earth dwellers" is used in the Old Testament it is rightly translated "land dwellers" or "inhabitants of the land" since the context references a localized area of land or country like Israel. However, in a global context, the same Hebrew phrase is best rendered "inhabitants of the earth" (Psa. 33:14; Isa. 18:3; 24:6, 17; 26:21; Jer. 25:30; Joel 2:1; Zep. 1:18). All five uses of "inhabitants of the world" appear to be in a global context (Psa. 33:8; Isa. 18:3; 26:9, 18; Lam. 4:12) and in all but one instance (Lam. 4:12) are used in the same context with "earth dwellers." When "earth dwellers" and "world dwellers" are used in the same contexts it serves to strengthen the notion that a global rather than local context is intended.
Every global use of "earth dwellers" in the Old Testament appears in a judgment context and probably all phrases also will take place in the future, during the day of the Lord or tribulation period. It is of special significance that both "earth dwellers" and "world dwellers" are used multiple times in Isaiah 24-27, often called "Isaiah's Apocalypse." Chapter 24 tells us that God's worldwide judgment will come upon all mankind because of specific sins of "the inhabitants of the earth" (24:5, 6, 17). Isaiah 26:9b says, "For when the earth experiences Thy judgments the inhabitants of the world learn righteousness." The final two verses of chapter 26 speak of the tribulation period. Verse 20 says that Israel will be hidden away and protected "until indignation runs its course." Since the remnant of Israel will be protected during the tribulation, then what will be God's purpose for the judgment of this period? Verse 21 answers that question as follows: "For behold, the Lord is about to come out from His place to punish the inhabitants of the earth for their iniquity; and the earth will reveal her bloodshed, and will no longer cover her slain." Thus, we see that a purpose for the tribulation will be to "punish" the earth dwellers. This is very similar to the statement in Revelation 3:10 that says the Lord will "test those who dwell upon the earth." It seems clear that Isaiah 24-27, and especially 26:21 provides the backdrop for understanding what is meant in Revelation 3:10, as well as John's use of "earth dwellers" throughout Revelation.
To Test The Earth Dwellers
Since one of the main purposes of the judgments of the tribulation are to "punish" (Isa. 26:21) or "test" (Rev. 3:10) the earth dwellers,  it is important to know what this means. The Greek word for "test" is peirazo, which means "to endeavor to discover the nature or character of something by testing, try, make trial of, put to the test."  It is important to keep in mind that a major purpose for the judgments of the tribulation in Revelation (4-19) are to test the earth dwellers under the most extreme circumstances in order to vindicate their rejection of the Lamb (Jesus) and His message (the gospel). No matter the severity of the judgments that are issued from heaven, not a single earth dweller repents (see Rev. 6:15–17; 9:20–21; 16:9, 11, 21).
The fact that not a single earth dweller repents in the detailed account of their testing in Revelation is likely the reason that the retributive term "punish" is used in Isaiah 26:21. Isaiah's prophecy pictures a finished evaluative conclusion, while John speaks of the purpose before it has produced a certain outcome. However, the subsequent events of Revelation make it clear that the testing of the earth dwellers vindicates God's judgment upon them.
Who Are The Earth Dwellers
When we survey the eleven uses of "earth dwellers" in Revelation, we see an interesting composite that develops. Not only are they to be tested in order show their true metal (3:10), they are clearly identified as those who are persecuting and killing believers during the tribulation (6:10). Many of the judgments of the tribulation are targeted for the "earth dwellers" (8:13). It is the "earth dwellers" who rejoice and send gifts to one another when the two witnesses are killed in Jerusalem during the middle of the tribulation (11:10). When the Beast (Antichrist) is introduced in Revelation 13, it is noted that, "all who dwell on the earth will worship him" (13:8, 12). Thus, 100% of the "earth dwellers" receive the mark of the beast and will spend eternity in the Lake of Fire. During the tribulation, as followers of the Beast, the "earth dwellers" will be deceived by the false signs and wonders of the Beast and will erect an image of the Beast, likely in the Jewish Temple (13:14). While the target of the preaching of the gospel by an angelic messenger will be "earth dwellers" (14:6), not a single one of them will follow the Lamb, instead they will wonder after the Beast (17:8).
Tony Garland correctly surmises that the term "earth dwellers" conveys a "soteriological/eschatological  meaning in the book of Revelation for it denotes the unsaved at the time of the end who steadfastly continue in their rejection of God."  Thus, "earth dwellers" are a moral rather than a geographical term, even though the phrase has a geographical connotation. "Earth dwellers" appear to be a figure of speech called a synecdoche, where the whole (earth dwellers) is put for one of its parts (unbelievers during the tribulation). 
"Earth dwellers" are contrasted to the proper focus in Revelation upon the heavenly temple, from where God's orders go forth in order to establish the Kingdom of God upon earth. Instead, the focus and ambitions for the "earth dwellers" are limited to the earth and not God's will, which is issued from heaven and enacted upon the earth. "This fact explains," notes Garland, "why the events of Revelation include great judgments poured out upon the natural systems of the earth for the earth has become an idol of worship for the earth dwellers."  "In contrast to the faithful who are aliens and sojourners upon the earth (Lev. 25:23; Num. 18:20, 23; 1Chr. 29:15; Ps. 39:12; 119:19; John 15:19; 17:14, 16; Php. 3:20; Heb. 11:13; 1Pe. 2:11) and whose hope is heavenward (Heb. 11:13–16; Rev. 13:6), these that dwell upon the earth are trusting in man and his environment."  Renald Showers tells us: "All of these Revelation references to 'them that dwell upon the earth' clearly indicate that they will be unsaved people of the future period of testing who will never get saved.... In spite of the devastating horrors of the sixth trumpet, which will kill one-third of mankind, the earth-dwellers will not repent of their wicked deeds (Rev. 9:20–21)." 
Luke 21:35, part of our Lord's Olivet Discourse about the end times, warns: "for it will come upon all those who dwell on the face of all the earth." In this instance, the "earth dwellers" will be the ones caught off guard by the judgment of the tribulation period. The same theme of unpreparedness is found in 1 Thessalonians 5 and the sons of darkness (5:1–11). They are unprepared because they have not trusted Christ as their Savior.
A similar passage, which does not use the term "earth dwellers" but almost certainly has in mind the "earth dwellers" by a different name (those who love not the truth), provides further insight into this matter. "And for this reason God will send upon them a deluding influence so that they might believe what is false, in order that they all may be judged who did not believe the truth, but took pleasure in wickedness" (2 Thess. 2:11–12). This statement reinforces the notion that a purpose for the tribulation includes a testing and judgment of the "earth dwellers." Here God is seen as the One who enables the man of lawlessness to produce false signs and wonders because they do not love the truth. Maranatha!
 From a search conducted by the computer program Accordance, version 7.4.2.
 From a search conducted by the computer program Accordance, version 7.4.2.
 The other main purpose of the tribulation is to lead to Israel's conversion and acceptance of Jesus as their Messiah (Isa. 26:11–20; Jer. 30:1–24; Ezek. 20:33–44; 22:17–22; Dan. 12:1–13; Zech. 12:10—13:1, etc.).
 Walter Bauer, A Greek-English Lexicon of the New Testament and Other Early Christian Literature, a translation and adaptation by William F. Arndt & F. Wilbur Gingrich (Chicago: The University of Chicago Press, 1957), p. 793.
 Soteriological means the study of the doctrine of salvation, while eschatological means the study of the doctrine of last things.
 (italics original) Tony Garland, A Testimony of Jesus Christ: A Commentary on the Book of Revelation, 2 vols. (Camano Island, WA: SpiritAndTruth.org, 2004), vol. 1, pp. 264-65.
 See Ethelbert W. Bullinger, Figures of Speech Used in The Bible (Grand Rapids: Baker Book House,  1968), pp. 637–38.
 Garland, Revelation, vol. 2, p. 281, e.n. 77.
 (italics original) Garland, Revelation, vol. 2, p. 265.
 Renald E. Showers, Maranatha, Our Lord Come (Bellmawr, NJ: The Friends of Israel Gospel Ministry, 1995), p. 265 as cited in Garland, Revelation, vol. 2, p. 265.