You set-up your account and at the beginning you are allowed to send 5 postcards at a time. When you click "send a postcard" you are provided with the address of a random person who lives somewhere in the world (there are options to send internationally and domestic or just internationally). You send these people postcards (sometimes their profiles request certain types like flowers, lighthouses, b&w, etc.) and when they mark your postcard as received, you then get added to the worldwide recipient list and will soon get a postcard from a total stranger. The more you send, the more you are able to have traveling at once (I can send 13 at a time now).
As of today, I have been a Postcrossing member for 784 days. I have sent 231 postcards and have received 219 glorious postcards from places all over the world!
I honestly think postcards are a great thing to collect because they are small, easy to take care of (hello, shoebox!), and they are cheap. Cheap being important here so friends/family on any budget can easily afford to send me one when they are traveling without dipping too heavily into their funds.
Out of Postcrossing, I have acquired 2 loyal pen pals with whom I hope to stay in touch for life. But what makes Postcrossing great is that you do not have to remain in contact with people you send cards to or receive cards from. If you have enough in common, obviously you can both decide to stay in touch, but usually, I don't.
You can also do a direct swap which is when you either find someone's profile and ask them to trade cards with you because you want a card from where they live, or you just trade with someone you received a card from.
Today in the mail, I received a postcard from Janneke who lives in The Netherlands. I had sent her a Postcrossing card a few weeks ago. She sent me an awesome card from Amsterdam. On the back of the card she wrote "I'm not from Amsterdam, but who cares?" and I just thought that was adorable! The card is pretty amazing too! Behold!