When acting unhesitantly, you're not indecisive or unsure. You don't stop to think about whether you should or shouldn't do something. You're certain about what you're doing, and you're willing to do it.
In certain situations, acting unhesitantly is not a wise thing to do. Running unhesitantly across four lanes of traffic to catch a baseball cap that flew out of your car window would be foolish and unsafe. But acting unhesitantly in other circumstances can save the day. Swinging unhesitantly at a baseball in the strike zone could yield a game-winning home run. Dashing unhesitantly to pull a small child out of harm's way could save a life!