An instance is a specific example or case of something. One instance of being chased by a growling dog can make a person spend his whole life being afraid of animals.
It's common to find instance used in the expression "for instance," meaning "for example." Bright colors — for instance, pink, green, and blue — can cheer you up when you're feeling sad. Instance can also mean "occurrence." Several instances of cheating might be reported after a math test, for example. In the sixteenth century, the Medieval Latin word instantia meant "example to the contrary," leading to an early definition of instance as "single objection."