The verb starve means suffering or death caused by a lack of food, though people also use it as a dramatic way to say they are hungry, as in, "If we don't start cooking dinner now, I think I'll starve."
The word starve has origins in the Old English word steorfan, meaning “to die.” It is true that if you don't eat for a period of time, you could starve, meaning die from hunger. Today, starve is also used to describe less severe limitations on food, such as when you tell your friend, "I have to go to lunch now. I'm starving." This is a way of describing discomfort caused by hunger.