Why do people feel hungry?

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It's related to several things. One is glucose level. No matter how much you eat or drink, if your blood sugars drop too low, you'll feel hungry and shaky.
Another reason is your stomach. Your stomach gets used to being a certain size, and being filled with a certain amount at certain times. If you go without eating for too long and let your stomach shrink, it sends your brain signals telling you to eat. This is also why you can curb this particular hunger impulse by drinking large amounts of water.

And because our ancestors were opportunistic eaters (they gorged when they could get food, because they didn't know how long they'd have to go without), we can actually become hungry because of outside stimuli. Smelling delicious food cooking, or watching a commercial for your favorite resteraunt, for example.
The last explanation isn't really about hunger for food, but for emotional relief. When some people get stressed or lonely or angry or sad, they will have an almost irresistable urge to eat. This is because the act of eating triggers pleasure centers in the brain. It's an instant high. It makes sense if you think about it, often the first sensation of pleasure a newborn gets is from nursing.