These words sound very similar, and all express the underlying feeling of security and safety; however, they are used quite different.
Assure is the only one of the three words that means “to reassure someone or to promise.” I assure you that your car will be ready by tomorrow. I assure you that the fish was caught today.
Ensure basically means “to make certain or to guarantee.” The teacher did his best to ensure the students were ready for the exam.
Insure can be interchanged with ensure in some cases, but it is simplier to keep the meaning of these words clear by using insure only when talking about insurance. It only costs $150 a month to insure your whole family.