To hesitate is to pause before doing something, often out of concern or worry.
If you're playing basketball and have a wide-open shot but don't take it right away, you hesitated. Maybe you felt too much pressure to shoot the ball. When people are nervous or worried, they tend to hesitate. Hesitating while speaking is common. In class, if you're not sure you have the right answer, you'll hesitate. When giving bad news, people often hesitate. Sometimes it makes sense to hesitate and sometimes you just need to do what you have to do.