An assurance is a vote of confidence. If you give your friend an assurance that you'll be there, you'd better show up.
If you pledge to do something or make a binding commitment to do it, you can use the noun assurance. If the bank is going to loan you money to buy a house, they are going to need some sort of assurance that you will repay the loan in a timely manner. If you have confidence in yourself and your abilities, you can also use assurance to describe that — "The baseball team played with assurance, quickly racking up a seven point lead."