Here is a link to their
help section.
It is a means to transfer funds over the internet. It is probably most commonly used on eBay, but other companies and individuals use it as well. Just the other day, a buddy of DH's paid him $40 he owed him via paypal rather than write a check.
Personal paypal accounts are free, while premium/ business types are not. My DH's is a personal and mine is a premium-- that way I can take credit cards on eBay and he can get money from his friends without associated fees.