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."
Primary Meanings of assurance
a binding commitment to do or give or refrain from something
a British term for some kinds of insurance
n a binding commitment to do or give or refrain from something
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guarantee, warrant, warrantee, warranty
a written assurance that some product or service will be provided or will meet certain specifications
an unconditional commitment that something will happen or that something is true
a solemn pledge of fidelity
a solemn pledge (to oneself or to another or to a deity) to do something or to behave in a certain manner
a guarantee that an obligation will be met
a payment given as a guarantee that an obligation will be met
a written certificate that gives the holder the right to purchase shares of a stock for a specified price within a specified period of time
a guarantee of professional or financial security
full faith and credit
a guarantee to pay interest and principal on debt; usually issued by the United States Treasury