Basically, PayPal is an electronic money transferring agent. Their system works like an online bank. You can transfer money into your PayPal account. Then you can send it to whoever you wish (note that there are certain things you can not use Paypal for, such as sending someone money for personal use). When you send money to paypal, it is stored in one of the banks Ebay uses for money storage and is linked to your account via paper documents and electronic documents. All money is FDIC ensured just like a bank up to $100,000.
There are no hidden fees about Paypal. The basic account is completely free, but can not accept Credit Card Transfers (you can send them, however). The Premier account can accept Credit Card payments, but a fee of 2.2% + $0.30 is charged to the transation.
The only bad thing I have found with Paypal is that transfers take 3-5 days if you are transferring from a checking account. Other than that, I haven't had any problems with them.