To assure someone is to remove someone’s doubts. In other words, to tell someone that something will definitely happen or is definitely true so that they are less worried. Example: Her doctor has assured us that she’ll be fine.
To ensure something is to make sure it happens—to guarantee it. Example: They want to ensure (=make sure/ make certain) that the building is safe before entering it.
To insure something or someone is to cover it with an insurance policy. Example: Have you insured your car? Does it have insurance?
Some people use assure, ensure, and insure interchangeably. All three verbs have something to do with “making sure” and are therefore similar, but each of them has a distinct meaning.