If you assure your boss that you’ll finish your project by Tuesday, you are make a promise or commitment to have it done by Tuesday.
The verbs insure and ensure look and sound like assure but they aren't synonyms. There is some overlap in meaning — all of them can mean “to make secure or certain” — but assure is generally used in situations when you are referring to a person: “I assure you that I haven’t forgotten about driving you to the airport” or “He called his mother to assure her that everything will be fine.”