The two primary advantages of Point and Shoot cameras over SLR cameras are their small/lightweight size and simplicity. You just point them at the object you wish to photograph, and shoot. They typically have a nonremoveable zoom lens, with autofocus and flash, and minimal controls.
The two obvious disadvantages that Point and Shoot cameras have versus SLR cameras are the lack of a high quality and/or interchangable lens, and the lack of sophisticated programming controls.
You can take some very good quality photos with a Point and Shoot camera, perhaps even an excellent photo every now and then. Just don't expect to consistently take professional quality photographs with one.
Generally, any camera that does not have an interchangeable lens falls under the Point and Shoot category. That applies to both digital and film cameras.
External LinksDPreview.com - indepth review of digital Point and Shoot cameras.