The country's in the midst of civil war and the leader of one party, David, sends to Abigail's husband for food for his army. Her husband refuses outright. Luckily for him one of his servants runs to Abigail to see if she can fix things, because a) David's been really polite, not taking anything without asking and making sure his soldiers don't loot the place, and b) this doesn't mean he'll carry on being so polite.
Abigail (as the servant expected) knows what to do. She ignores her husband's orders and goes to meet David with five of her handmaidens and donkeys laden with food. She makes a long speech:
"Pardon your servant, my lord, and let me speak to you; hear what your servant has to say. Please pay no attention, my lord, to that wicked man Nabal. He is just like his name—his name means Fool, and folly goes with him. And as for me, your servant, I did not see the men my lord sent. And now, my lord, as surely as the Lord your God lives and as you live, since the Lord has kept you from bloodshed and from avenging yourself with your own hands, may your enemies and all who are intent on harming my lord be like Nabal. And let this gift, which your servant has brought to my lord, be given to the men who follow you.
Please forgive your servant’s presumption. The Lord your God will certainly make a lasting dynasty for my lord, because you fight the Lord’s battles, and no wrongdoing will be found in you as long as you live. Even though someone is pursuing you to take your life, the life of my lord will be bound securely in the bundle of the living by the Lord your God, but the lives of your enemies he will hurl away as from the pocket of a sling. When the Lord has fulfilled for my lord every good thing he promised concerning him and has appointed him ruler over Israel, my lord will not have on his conscience the staggering burden of needless bloodshed or of having avenged himself. And when the Lord your God has brought my lord success, remember your servant."
And David blesses her good judgement, accepts the gift and decides not to murder all the men of the household after all.
When Abigail goes home Nabal's drunk, so she waits until morning to tell him. At which point "his heart failed him and he became like a stone" and ten days later he dies. When David hears of this, he sends to ask her to become his wife (I'm guessing partly considering himself responsible in a 'he totally deserved it' way for Nabal's death, and partly super impressed by Abigail). She accepts and goes to him with her five female servants, thus becoming his third wife though at this point Michal is off with her other husband.
Later events in Abigail's life:
She travels with David and his first-apart-from-Michal wife Ahinoam into exile to avoid Saul. (1 Samuel 27:3) While there she's captured by the Amalekites; (1 Samuel 30:5) and carried away with them until David kills them and rescues her and Ahinoam. She returns with him when he's anointed king of Judah. (2 Samuel 2:2) There she gives birth to his second son (named either Kileab (1 Samuel 3:3) or Daniel (1 Chron 3:1), oh biblical inerrancy!)