When the stinger pierces the skin of a human or an animal, like a skunk, bear or raccoon, it sticks because it has little barbs on it that catch and hold on flesh. When the bee flies away, her stinger is torn away, along with the end of her abdomen, and often some of their insides too.
Honey bees can sting other insects many times without dying because the stinger's barbs won't stick in insect flesh because it's so pulpy.
Okay, that's the scientific part. But the human part is, "OUCH! That hurt!"
What to do if you've been stung:
Bees don't bite, so the term "bitten by a bee" or "bitten by a wasp" isn't true. Their mouth parts aren't big or strong enough to do much biting. When these stinging insects are going about their business flying around, their stingers are retracted inside their bodies.