1 : to hold back in doubt or indecision
2 : to delay momentarily : PAUSE
transitive verb: to hold back from in doubt or uncertainty <wouldn't hesitate to commit herself>
[M-W's Col. Dic.]

1: Does to hold back in doubt or indecision mean the same as to hold back because of doubt or indecision?
2: What does ''wouldn't hesitate to commit herself'' mean?
1. Yes.

2. "To hesitate" = "to hold back." The opposite, "to commit onesself," is to be decisive. (You make a decision and commit yourself to abide by/with the consequences of that decision - at least, until you change your mind.) To fail to commit onesself is to be indecisive. A decisive person would not hesitate to commit herself. An indecisive person would hesitate to commit herself, and would hold back in doubt and indecision.

- A.
intransitive verb

1 obsolete: to perpetrate an offense
2 : to obligate or pledge oneself
[M-W's Col. Dic.]

Thank you, Avangi.