The Apochypha is specifically referenced in Latter-day Saint doctrine. Joseph Smith prayed to know if he should revise the translation of the Apocrypha and here is the response in full:
"Verily, thus saith the Lord unto you concerning the Apocrypha—There are many things contained therein that are true, and it is mostly translated correctly; There are many things contained therein that are not true, which are interpolations by the hands of men. Verily, I say unto you, that it is not needful that the Apocrypha should be translated. Therefore, whoso readeth it, let him understand, for the Spirit manifesteth truth; And whoso is enlightened by the Spirit shall obtain benefit therefrom; And whoso receiveth not by the Spirit, cannot be benefited. Therefore it is not needful that it should be translated. Amen" (D&C 91).
The Apocrypha isn't completely absent from Latter-day Saint discussion, Elder Holland quoted from it in his talk The Tongue of Angels, but it's pretty close. Many Latter-day Saints probably don't even know what it is, which of course suggests that even more don't know what it contains. As an aside, when I served my two-year full time mission in Las Vegas, Nevada, a faithful Catholic debated the value of the Apocrypha and expressed his utter incredulity that it wasn't a part of our canon. Especially since that experience, I have had a lingering desire to read the Apocrypha and know for myself what it contains.
The King James version of the Apocrypha, which is the version I read, reads and feels like the Old Testament. In fact, considering most people's lack of familiarity with the Old Testament, I would posit large portions of the Apocrypha could be read to a group of contemporary Christians, Latter-day Saints included, and they wouldn't be able to determine the source as the Old Testament or the Apocrypha. As familiar as the language is, the stories, whether true or not, are unique and, for the most part, quite interesting.
Perhaps one of the largest contributions the Apocrypha makes to established biblical canons is the inclusion of more stories in which women are key players or a major focus. There is an expanded story regarding Esther and entirely new stories about a woman named Judith and Susanna. The book of Judith is particularly meaningful for women since it shows a woman not only in a position of authority but one who demonstrates great courage and faithfulness. The book The History of Susanna centers more around legal and ethical justice rather than womanly triumph but is nonetheless an important story about protecting the innocent.
The other books throughout the Apocrypha follow similar patterns present in the Bible, such as: a collection of pithy sayings and words of wisdom, historical accounts of corrupt leaders, people, and the inevitable justice of God, and heavenly visions and visitations. If you've read and studied the Bible, you'll be right at home. The interesting exercise, especially as a Latter-day Saint, is attempting to determine what is inspired and what is not. I certainly didn't make any kind of extensive and prayerful examination of the text and its spiritual truthfulness, but I did find valuable spiritual insights which are more than likely true. (Coming back to Holland's talk, if he feels comfortable enough to quote from it in General Conference we can be assured at least some of it is true just as Doctrine and Covenants section 91 states). On the other hand, I could see, especially in the second book of Maccabees, some curious and frankly out of place commentaries which gave me pause regarding their veracity. Just as the first book of Maccabees states: "Also that the Jews and priests were well pleased that Simon should be their governor and high priest for ever, until there should arise a faithful prophet" (Emphasis added). Without a prophet, who is actually doing the writing and is it actually endorsed by the Lord?
In the end, the Apocrypha is a fascinating addition to existing scriptural knowledge, albeit unnecessary from a devout Christian's perspective. It doesn't reveal too much regarding the Christian faiths, mostly because there are so many Christians who don't accept and embrace it in the same way they do the Bible. I enjoyed reading it and love being able to say I have, but I have no plans to continue my study of it.
Other Topics of Interest:
Brow Bruising Reads
The Hardest Book I have Ever Read