It comes from a literal interpretation of the Old Testament.

The book of Genesis contains several genealogies in chapters 5 and 11 which list the age each person was when he fathered the next person listed. Since the first person was Adam, and he was created on Day Six of the world, you can add up these ages to show that Abraham was born in 2008 AM (Anno Mundi: Year of the World.) Using other chronological figures in the Bible, you can calculate the Anno Mundi dates of various events in the history of Israel which secular historians have also dated in the conventional BC system. So, according to this literal interpretation of the Old Testament, the world was created c. 4000 BC - 4004 BC, by the famous calculations of Archbishop Ussher.

I give an approximate date for two reasons. First, the secular dating of Near Eastern events that anchors this chronology is approximate - as are all other dates earlier than several centuries BC, save for a very few things such as eclipses. Second, there's one dispute about whether the 430-year figure in Exodus 12:40 counts only the time in Egypt or all the time since Abraham expelled Ishmael; most scholars such as Archbishop James Ussher and Rabbi Yossi ben-Halafta have agreed on the latter. At most, however, these disputes would move the age of the world by a couple centuries.

Many modern Christians don't agree with this interpretation of Genesis. One interpretation is to say that "Reu lived two and thirty years, and begat Serug" means that Reu was 32 years old when he fathered the son who was the distant ancestor of Serug - which lets there be any number of generations, and years, in-between each person named. Another interpretation is to accept that Adam was born c. 4004 BC, but deny that he was the first human in a biological sense. Still another interpretation, of course, is to deny that these genealogies relate to any genealogical line of descent at all.

However, these genealogies form the foundation for the young-earth Creationist movement, which does interpret them quite literally.