First we must lay out two basic interpretive principles. Then I will list the meaning of the 144,000 (Revelation 7:4-8; 14:1-5) for each of the four main Christian interpretive approaches to the book of Revelation.
First we must decide if the 144,000 mentioned in Revelation 7:4-8 are the same as those in 14:1-5, or if they refer to separate groups. Early Christians such as Origen understood these to be the same, but some dispensational theologians do not believe that this is the case.
We then have essentially two interpretive choices remaining: to interpret the number symbolically or literally. Assuming both Revelation 7 and 14 refer to the same group, they are either literally 12,000 Jewish male virgins from each tribe or they are symbolically the people of God. There are good arguments on both sides of the fence, but we must be consistent with the approach chosen. For instance, a literalist who believes both Revelation 7 and 14 refer to the same people should not take the number 144,000 literally without also taking the ethnicity, gender, and celibacy of these individuals literally as well.
Four Main Perspectives
All of these approaches are inherently symbolic except for the futurist approach, which is literal (although some futurists also believe the number to be symbolic).
Historicists associate the 144,000 with the Church. They believe the number is symbolic and indicates the totality of the Church.
Preterists believe that 144,000 is a symbolic number of Jewish Christians who escaped the destruction of Jerusalem in 70 A.D.
Futurists claim that the 144,000 are either a remnant of the Jewish people (literal) or the last generation of Christians alive during the Tribulation (symbolic).
Idealists consider the 144,000 to be a symbolic number representing all God's people throughout all history under the old and new covenants (i.e. spiritual Israel).
Origen, "Origen’s Commentary on the Gospel of John", trans. Allan Menzies In, in The Ante-Nicene Fathers, Volume IX: The Gospel of Peter, the Diatessaron of Tatian, the Apocalypse of Peter, the Visio Pauli, the Apocalypses of the Virgil and Sedrach, the Testament of Abraham, the Acts of Xanthippe and Polyxena, the Narrative of Zosimus, the Apology of Aristides, the Epistles of Clement (Complete Text), Origen’s Commentary on John, Books I-X, and Commentary on Matthew, Books I, II, and X-XIV, ed. Allan Menzies (New York: Christian Literature Company, 1897), 297-98. The relevant sections referenced in this answer can be read for free online here and here.
John D. Barry, Michael R. Grigoni, Michael S. Heiser et al., Faithlife Study Bible (Bellingham, WA: Logos Bible Software, 2012).
For a detailed report on how this has been interpreted in Church history see this great article.