Paypal is essentially a service for "regular people" to transfer money to one another fairly easily. They got their start as one of the payment options accepted by Ebay 5-7 years ago. Since then, Ebay has bought them out and expanded their capability - which is a testament to the ease of the Paypal process as well as the tight security measures they take with the millions and millions of transactions that occur through Ebay.
To start, you can have Paypal pull money out of your credit card and put it in an "account" (it's not a bank...SEC filings, etc...) and you send it to another account via the recipient's e-mail address.
If you plan on receiving funds, the way to go is set them up with your checking account where they can make direct deposits at no cost for personal transactions (Ebay transactions have a processing fee).
Knowing that Paypal has both buyer and seller information, it kinda keeps everyone "playing nice". I've used paypal for over 100 transactions and have had ZERO problems.