There are 498 different threads on here in which you can find more details (just do a search for Photopass), but here are the basics:
Go to any of the parks, find a staff photographer standing around taking pics in front of a landmark or at a character spot, ask the first one for a Photopass card (which you'll keep and use throughout your trip), and keep presenting that card to each photographer for whom you wish to pose. Once your trip is done, go online to DisneyPhotoPass.com, enter the number from that card, and see the photos that were taken. It's free to have the photos taken, but then you have to pay for individual downloads, a CD that contains all the ones you want, or individual prints. Also, you can have a book or other merchandise printed with the photos you like.