Well...they don't.
They accept a group of documents known as "the Deuterocanon".
Not included in the Deuterocanon: 1 & 2 Esdras and The Prayer of Manasseh
(Those documents normally ARE included in the English Apocrypha.)
They accept the Deuterocanon because that was the official decision made at The Council of Trent.
Why was that the official decision made at the council of Trent?
My OPINION as to why the council of Trent made that decision:
#1
All of those documents were explicitly authorized (approved) in early councils, namely: The Council of Laodicea and The Council of Carthage. Since 1 & 2 Esdras and The Prayer of Manasseh were not explicitly authorized in any early councils, the Roman Catholic Church rejected them.
#2
Excepting The Book of Baruch (approved at The Council of Laodicea), all of the other documents in the Roman Catholic Bible had been included in the Latin Vulgate (the book that was first actually called "the Bible") since the oldest copies of the Vulgate that the officials at Trent knew.
SO, in other words (in my opinion), their thinking was:
A - All of these documents have been included in the Vulgate since its origin
- - - except for Baruch, which had been included for only a few centuries as of the time of the Council of Trent
B - All of those documents, including Baruch, were approved by 4th century Councils
- - - that is to say: even before the first Vulgate was produced
C - Therefore, all of those documents have been approved since ancient times, officially, and are therefore both by tradition and by previous official ruling part of the Bible
More info:
http://www.bible-reviews.com/charts/history-western-bible-canons.php