SPF stands for Sun Protection Factor. It's the way the FDA measures the amount of protection that sunscreen provides. SPF only tells you how much UVB protection you're getting, and not UVA. The number next to the SPF means how much more time you're allowed to be in the sun without getting red.
For example, if it takes you five minutes to get red in the sun by wearing something like SPF10, it will take you 15 minutes to get red in the sun. It's important to note that the amount of UVA exposure you are getting in this time is not measured by the SPF. So it's important to pay attention to that in the sunscreen you buy, not only it has SPF rating, but also mentions the amount of UVA protection you're getting.
Currently, the FDA does not have a standardized system to regulate how much UVA protection you're getting, but that is about to change.