As soon as you download it it'll scan your hard drive(s) for all pictures, videos and other media and place it into a library initially organizing by date and time (you can sort by name also but I prefer the date). As soon as it's done that you can start organizing by excluding or including additional folders to monitor; scan once, ignore and scan constantly.
Here's where it got fun for me; I began to tag my family and friends in a couple of the pictures. As soon as you have done one or two it starts scanning through your pictures automatically and adding them to people albums. The facial recognition of Picasa is very cool although it doesn't do so well on kids as their faces change more frequently over time.
Another great feature of Picasa is the gold star attributes you can add to your favorite pictures so you can create a highlight of a specific batch of photos and only view these (e.g."Mexico highlights" ignoring the random pictures of drunk people and blurred shots).
So that's Picasa as an overview but there are loads more options to organize and edit your photos. If you haven't got a good method for sorting out your online photos download this now!!
P.S. Always backup your photos!! (you can even back them up to Google's storage service which gives you about 200GB for $50 a year. With Picasa you can then synch up all your photos automatically to this site. It's great if you were to have a hard drive go bad or a fire!) If Jason recommends it then it must be a good thing!!