Assure + SOMEONE To give someone confidence or hope concerning a particular outcome/result eg. John assured his daughter that he would be home for dinner. eg2. I will pay back the money, I assure you! Ensure + A RESULT/OUTCOME To make certain or increase the chance of a particular outcome. eg. The farmer locks the gate to ensure that the animals don't escape. eg2. My sister was very kind to my father to ensure that she would be written in his will.

To ensure is to take steps in order to make something safe or certain (to ensure the safety of your children, your pension will ensure a worry free retirement). To assure is to tell someone that everything is going to be OK in a way that they feel certain that it's going to be like that. I should mention that I've heard assure used for the purpose of "ensuring" but it's usually like I defined it above. While you're at it, to insure is to cover something with insurance, like a car insurance or your health, with an insurance policy.