"21 Grams" is done in the Quentin Tarantino "all the scenes are out of order" style, which is a good way to tell this story.
Paul Rivers (Sean Penn) is a college math professor and a long-time smoker who is close to death from heart failure. He's weak, coughs and gasps, and drags around an oxygen tank to help him breathe. He's on the transplant list for a new heart. His wife wants nothing more than to get pregnant by him before he dies.
Jack Jordan (Benicio Del Toro) is an ex-con that has spent more time in jail than out, but has reformed and is working in a church, spreading the gospel, and helping kids that are heading toward the same kind of trouble he's been in. He and his wife have two young children.
Cristina Peck (Naomi Watts) seems to be a typical housewife. She and her husband have two young daughters, and they appear to have an ideal life.
One afternoon Jack accidentally runs over Cristina's husband and daughters while they're out walking. Both of the little girls are killed, and the father ends up brain dead. Cristina consents to organ donation, and her husband's heart ends up being transplanted into Paul.
Jack turns himself in for the hit-and-run and goes to jail, but is later released. Paul recovers and hires a private detective to find the donor family (to find out "who he is"). The detective comes up with the information not only about the donor and his widow, but also about the ex-con. Most of the movie is about the relationships that develop between these three main characters.