Here is a comparison of my cameras. They are, from left to right, a Canon 60D, an Olympus e-pm1 (pen mini), and a Canon S95.
The Canon S95 is compact camera. It is the size of a point and shoot. This camera is definitely pocketable. At the time, it had the largest sensor in a body this small. The sensor size is 1/1.7". It provides a little more functionality than a typical point and shoot, as it has modes for Aperture priority, Shutter priority, and full manual. It takes pretty good pictures, especially for a compact. As the ISO increases, the quality goes down pretty fast. It takes excellent quality at ISO 200. The lens is fixed. It has a nice fast aperture of 2.0, but only at its widest zoom.
The Canon 60D is a DSLR, with an APS-C sized sensor. It takes amazing pictures. The quality of its images are clearly better than the other 2 cameras. Its capable of taking excellent quality images through ISO 800, and really good quality through ISO 1600.
The Olympus e-pm1 is a micro four thirds camera. The sensor is smaller than APS-C, but is still pretty big, and a lot larger than 1/1.7. The body size is like a compact, but the lens sticks out, so its just a bit too large to be pocketable. Like a DSLR, this camera has an interchangeable lens system, using the micro four thirds mount. Also like a DSLR, this camera has a hot shoe, so external flashes can be used. The camera is capable of taking excellent quality images through ISO 500, and good quality through ISO 800.
The micro four thirds camera is a great compromise between size and image quality. It is closer in size to a compact, and is closer in image quality to a DSLR.
Image sensor sizes, from the wikipedia article
Image sensor format: