These Books, and parts of Books, which the Orthodox and Coptics have as well, are referred to as the Old Testament Deuterocanon (or usually, just "the Deuterocanon") by us, and as "the Apocrypha" by Protestants who reject them. The Protestant Old Testament is patterned off of the Hebrew versions of the Old Testament, while the Catholic, Orthodox, and Coptic Old Testaments are modelled off of the Greek versions.
If you've ever discussed the reasons for their rejection with someone knowledgable enough to have a reason, there tend to be two common points brought up:
(1) the Jews don't consider these books canonical (by which, they mean modern Jews), and
(2) Jerome rejected them.
The first point is pretty weak. The Jews up to the latter half of the first century A.D., past the time of Christ, had no settled canon. And the Church has fulfilled the mantle of Israel, as the Old Testament repeatedly prophesied. While the Jews still have a particular role in God's plan of salvation, that role doesn't include setting the canon for Christian Bibles.
The second point takes various forms. Sometimes, they'll cut right to Jerome, while othertimes, the argument will be presented as if the speaker knows of someone prominent Church Father besides Jerome who felt this way. Occassionally, you'll even hear that "the early Church" rejected these books, but that's just untrue. In fact, if you read what Jerome actually says on the subject, you'll quickly realize that he acknowledged his own view as (a) the minority view, (b) opposed to the Church's view, and (c) possibly wrong, even sinfully so. The best evidence for this comes in his book Against Rufinus.
Here's the context. St. Jerome translated the Vulgate for the pope, at his request. And Jerome submitted to the pope's authority, including the entire Deuterocanon along with the rest of Scripture. But in his prefaces for some of the books, he noted criticisms that either he, or Jewish friends of his, had against the Greek versions (since by this time the Jews exclusively used the Hebrew version, and rejected the Deuterocanon). For these prefaces, amongst other things, Rufinus attacked him, and Jerome responded.
Jerome gets to his explaination of Daniel, and makes it clear that while he doesn't like that the Catholic version is based on a heretic's translation, he's willing to submit to the "judgment of the churches":
I also told the reader that the version read in the Christian churches was not that of the Septuagint translators but that of Theodotion. It is true, I said that the Septuagint version was in this book very different from the original, and that it was condemned by the right judgment of the churches of Christ; but the fault was not mine who only stated the fact, but that of those who read the version. We have four versions to choose from: those of Aquila, Symmachus, the Seventy, and Theodotion. The churches choose to read Daniel in the version of Theodotion. What sin have I committed in following the judgment of the churches? But when I repeat what the Jews say against the Story of Susanna and the Hymn of the Three Children, and the fables of Bel and the Dragon, which are not contained in the Hebrew Bible, the man who makes this a charge against me proves himself to be a fool and a slanderer; for I explained not what I thought but what they commonly say against us. I did not reply to their opinion in the Preface, because I was studying brevity, and feared that I should seem to he writing not a Preface but a book. I said therefore, "As to which this is not the time to enter into discussion." [...] Still, I wonder that a man should read the version of Theodotion the heretic and judaizer, and should scorn that of a Christian, simple and sinful though he may be.
Nota bene: the important thing, in the end, wasn't whether the Jews used that version (they didn't), or whether Jerome's individual reasoning and experience lead him to that conclusion (it didn't), or even what the standard Greek Septuagint said, but what the Church said. Understand that point, and the entire Deuterocanonical debate is settled. The Church closed the canon long before the Reformation, and no individual Christian (whether Jerome or Luther) has the authority to overrule Her Holy Spirit-protected judgment.