A non-compete agreement restricts someone, typically an employee, founder, or someone selling a business, from working for or starting a competing business for a set period of time and within a defined geographic area after leaving.
Enforceability varies enormously by state. California, for example, voids nearly all employee non-competes outright, while many other states will enforce them if they're reasonable in scope, duration, and geography. A non-compete written for a company operating nationally needs to account for the fact that it may be unenforceable in some of the states its employees actually live in.
Non-competes tied to the sale of a business are treated differently, and much more consistently enforced, than employee non-competes, since they're seen as protecting the value of what was actually purchased rather than restricting an ordinary worker's ability to earn a living. Worth keeping that distinction in mind when negotiating either side of an acquisition.
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