Premature means "not yet ready." Something that is premature arrives early, like a premature baby born before her due date, or the soggy cake you took out of the oven prematurely.
Premature is a simple word to break down. Pre means "early" or "before," and mature means "done" or "ready." If a decision is criticized as premature, it means that that decision was made too hastily, and probably would have been different if more time had been taken. If someone dies very young, you might say they died prematurely.