Its kind of a reference to heaven. "The poor man died and was carried by the angels to Abraham's bosom [or "side" depending on your Bible]."
Abraham is the father of, basically, the entire Jewish community. Remember he was promised that "your sons shall inherit the earth." Your could think of Abraham as a favorite of God. Well a few generations down the road, all Jews were considered descendents of Abraham, which is why Lazarus was brought to him, why the rich man begged with Abraham as "Father," and why Abraham called the rich man "Child."
My thoughts are that its possibly the 'waiting' or 'resting' place souls go until Christs return when they will rise up and be separated according to the choices made in life. Or perhaps its only souls of believers there and unbelievers souls rest elsewhere. We'll find out eventually.
The term "Abraham's bosom" is found only once in the New Testament, in the story of the rich man and Lazarus (Luke 16:19-31), in which Jesus was teaching about was the reality of heaven and hell. "Abraham's bosom" in this story is also translated "Abraham's side" (NIV, ESV), "next to Abraham" (CEV), "with Abraham" (NLT), and "the arms of Abraham" (NCV). These various translations speak to the enigmatic nature of the Greek word kolpos. All these translations are attempting to convey the sense that Lazarus went to a place of rest, contentment, and peace, almost as though Abraham (a highly revered person in Jewish history) was the protector or patron. In a sad contrast, the rich man finds himself in torment with no one to help, assist or console him. http://www.gotquestions.org/Abrahams-bosom.html