This is a pun on the word "raisin". This person desperately needed food, so their kids gave them a raisin to live. "Raisin" sounds like "reason". Giving food to a starving person is the "reason" why they live. Also, when people feel hopeless and want to give up on life, they may find something meaningful that gives them a "reason" to live. Often times that thing is someone who depends on you. For the starving person in the joke, that thing is their children.    
When I was starving to death , my children gave me a raisin to keep on living .