“This man has committed a crime.”
“Pet ownership is a big commitment.”
“I can’t buy this game because I’ve already committed this month’s spending money to our trip next week.”
“The project failed because the leader was not committed to making it succeed.”

“Commit” is often used instead of “do” for a crime. But it has another meaning, something like “promise”. If you get a pet or marry a person, you should be committed (or commit yourself) to taking care of the pet for the rest of its life or making the marriage work. If you have promised resources such as money or time for a certain project, you have already committed those resources, even if they haven’t actually been used yet. Now you have a commitment to provide the resources.