Growing up in the protestant evangelical persuasion means the Apocrypha might as well have meant "Apostate." I'd never read any of its books, even though some of the history it contains is relevant to understanding New Testament Jewish culture. In honor of Hanukkah this year, I decided to read 1 and 2 Maccabees for the first time. I learned a lot.
1 Maccabees was apparently written in Hebrew (wikipedia), though the only surviving text is Greek. 2 Maccabees (wikipedia) is believed to be entirely of Greek authorship. Both focus on the liberation of Jews living in modern-day Palestine during the 2nd century B.C. 1 Maccabees is longer and covers many more events in detail. 2 Maccabees moves more quickly and focuses on a four-year period.
They both read like a combination of the movies Braveheart and 300, in fact I can see how these books could have inspired certain scenes in both films. It reads like most men want the Bible to-- brave warriors standing up for God and slaughtering their oppressive enemies, liberating their people, and having their names echo in eternity. I can imagine that Mel Gibson was heavily influenced by the books, as further evidenced that he is making a movie about Judah Maccabee.
The conclusion of the movie Hoosiers features a locker-room scene with two pastors leading the heroic underdogs in a pre-game devotional. The senior pastor quotes (unattributed) from 1 Maccabees 3:19:
"For the victory of battle standeth not in the multitude of an host; but strength cometh from heaven."
The events of the books are believed to be prophesied in Daniel 11 & 12, when Antiochus IV Epiphanes rules Jerusalem and outlaws the Judaic laws, desecrates the temple, and massacres many Jews. This prophecy is repeated in the New Testament as a foreshadowing of the Antichrist. The horrors that the Jews experienced are gruesomely detailed. In 165 B.C., Judah Maccabee leads a revolt and kills Antiochus and various others who would take his place. The temple is cleansed, the idols torn down, and the sacrifice restored. This is where we get Hanukkah from, although the legend of the oil miracle is not recorded in the books. 1 Maccabees records the Jews' diplomatic outreach to a growing Rome while seeking protection from their neighbors. It records the in-fighting among the various post-Alexandrian factions and Israel being stuck in the middle. Eventually, Judah Maccabee is killed before an army of 20,000 invading Assyrians.
Jesus would have celebrated the Feast of Dedication (John 10) and it seems that many of His followers were expecting him to be the ultimate Judah Maccabee against the Roman Empire, instead of the Lamb of God being led to the slaughter. Reading 1 & 2 Maccabees helps me understand the expectations and disappointment of Jesus' followers.
Knowing that these books were included in the King James Bible and other early texts circulated also helps me understand a little of their influence on Christian culture through the centuries. We get various ideas and idioms in our English language from the Apocrypha via the King James (I read the books in their original King James. I recommend finding another translation). I would say the books also influenced whoever wrote the Book of Mormon, much of it reads very similarly.
In all, I recommend reading these as essential reading for anyone interested in learning more about Jewish and Middle Eastern history. I doubt you can really understand Hanukkah without them.