1. To be slow in doing something, or to pause while doing or saying something; often because of uncertainty or reluctance.
2. To be reluctant to do, or to say, something.
3. Etymologically, to hesitate means "to become stuck".

It comes from Latin haesitare, a derivative of haerere, "to hold fast, to stick".

The basic idea of hesitate refers to being "held back", or in speech of "stammering", and so of being unable to act or speak promptly or decisively.