Apocrypha may have different meanings depending on how it is applied to the Old or New Testaments and whether it is being used by Catholics, Protestants or Orthodox Christians. For the most part, the term apocrypha refers to any collection of scriptural texts that falls outside the canon. Since most English language bibles are from non-Orthodox sources, they sometimes are subtitled with Apocrypha meaning that it includes the Old Testament, so called Deuterocanonical Books that in the Orthodox Church are considered to be genuine parts of the Bible.
There are examples of false books from the Old Testament, there books are: Assumption of Moses, Ascension of Isaiah, Apocalypse of Elijah, Book of Enoch, Testament of the Twelve Patriarchs, and another Book of Maccabees. These books are not in the Old Testament canon of any church (with the exception of the Book of Enoch being canon to the Ethiopian Orthodox).
At the turn from the first century, many false writings about Christ were produced. These were the so-called apocryphal writings (not to be confused with the Old Testament apocrypha), also called pseudoepigrapha. These false writings carried the names of the apostles and introduced into Christian circles many fanciful and legendary stories about the childhood of Christ, the life of the Virgin Mary and the activities of the apostles.
With the pseudoepigrapha, there also appeared the false teachings of gnosticism, the Christian heresy which transformed Christianity into a kind of spiritualistic, dualistic, intellectual philosophy.
The Book of Enoch
The word of the blessing of Enoch, how he blessed the elect and the righteous, who were to exist in the time of trouble; rejecting all the wicked and ungodly. Enoch, a righteous man, who was with God, answered and spoke, while his eyes were open, and while he saw a holy vision in the heavens. This the angels showed me.
The Gospel of Thomas
These are the secret sayings that the living Jesus spoke and Didymos Judas Thomas recorded.
The Gospel of Peter
And they went and found the tomb opened, and coming near they looked in there; and they see there a certain young man sitting in the midst of the tomb, beautiful and clothed in a robe exceeding bright: who said to them, Wherefore are ye come? Whom seek ye? Him that was crucified? He is risen and gone.
Psalms of Solomon
The Psalms of Solomon is a group of eighteen psalms that are not part of any scriptural canon (they are, however, found in copies of the Peshitta and the Septuagint). The 17th of the 18 psalms are noteworthy for their Messianic value.