Three words, one sound, and a division that holds up well once you see it: "assure" takes a person as its object, "ensure" takes a result, and "insure" belongs to insurance. British usage sometimes lets "insure" cover "ensure," but the person-versus-outcome split between the first two is worth keeping in any register.
A verb. To tell someone something confidently, to remove their doubt. It takes a person as its object.
A verb. To make certain that something happens. It takes an outcome as its object.
Quick way to remember
Ask what follows the verb. A person follows "assure" — you assure someone. A result follows "ensure" — you ensure something happens. And if money changes hands against a risk, it is "insure."