Assure means “to convince” or “to guarantee” and usually takes a direct object.
Example: If we leave two hours early, I assure you that we will arrive at the concert on time.
Insure means “to guard against loss.”
Example: Before he could leave for his trip, Steve had to insure his car against theft.
Ensure means “to make certain.”
Example: Our company goes to great lengths to ensure that every product that leaves the warehouse is of the highest quality.