Assure means to promise or to guarantee: “The mayor assured the city residents that justice will be done and all the eve-teasers will be put behind bars”.
Assure also means to make something certain: “Winning the literary award should assure her publisher that the novel will be a success.”
Ensure means to make sure or certain that something will take place: “We took steps to ensure the safety of the cricketers on the Pakistan tour.” It also means to make safe or secure: “The government took steps to ensure the people that they would be safe from tyranny and terrorism.”
Insure, on the other hand, means to buy insurance for something; such as, property or health: “They want to insure their house and car against fire and flood damage.”
In the general sense, insure means to take steps or precautions for the safety of a situation; often done in an anticipatory or precautionary manner: “She bought a bag of sand for the sidewalk before the major storm to insure she was prepared for any icy conditions.”
If we have a close look at the three words, we observe that all of them include the meaning “to make secure or certain”. The use of assure refers to a person as in the sense of “to set the mind at ease”; as “she wanted to assure her employer that she was ready to handle the new assignment”.
A person can ensure that there will be prompt deliver of an item while insure is the only proper verb to use when someone means “to protect against loss”.
So, although ensure and insure can be interchangeable in some situations, insure is normally used in the sense of “to guarantee people or property against the risk of physical harm, damage, or loss” as when people have health insurance, property insurance, etc.