commit, committed, commitment

Definition:

The terms "commit" and "commitment" refers to making a decision or promising to do something.

A person who promises to do something is also described as being "committed" to doing it.
To "commit" to someone a certain task means to assign that task to that person. For example, in 2 Corinthians Paul says that God has "committed" (or "given") to us the ministry of helping people be reconciled to God.
The terms "commit" and "committed" also often refer to doing a certain wrong action such as "commit a sin" or "commit adultery" or "commit murder."
The expression "committed to him the task" could also be translated as "gave him the task" or "entrusted to him the task" or "assigned the task to him."
The term "commitment" could be translated by, "task that was given" or "promise that was made."