Assure means "to promise" or "to state with confidence":  "I assure you that we will be on time."  "I can assure you that nobody in this class will fail."

Ensure and insure are used interchangeably to mean "to make certain."  However, some authorities (including this writer) insist upon using only ensure in this sense, restricting insure to matters of legal and financial protection (i.e., to protect against loss).  Thus, these authorities would prefer ensure in:  "A good outline will help to ensure that an essay is well organized" and "We take every step to ensure that products are of the highest quality."  Most references state, however, that either insure or ensure could be used in these sentences.

Insure is always used when matters of legal and financial protection (i.e., insurance) are involved:  "In New Jersey, it is expensive to insure a car." "The young model wanted to insure her elderly husband's life for one million dollars."