Stretch Goals are a way to incentivize people to keep backing your campaign after achieving your original goal by adding more conditions to your original offer.
Your initial campaign goal is what you're trying to achieve for presenting your original offer. With Stretch Goals, you can add up to 3 more goal tiers.
For example, you can set up a Stretch Goal that states if $5,000 is achieved beyond the initial goal, then the target must agree to do something additional. Like wear a silly hat!