Overall Quality - In a well-exposed image with a full range of tones that do not require processing, the differences between, say, a TIFF file produced from your camera and one produced using Aperture’s Raw converter would probably be marginal. This is probably the
only situation in which there is little advantage to be gained from shooting Raw, but probably not one that occurs all that regularly for most photographers.
Bit Depth - Camera Raw files use the full number of bits (usually 12) available in the image data. If you shoot JPEGs, this is downsampled to 8 and the camera, not you, makes the decision about how effectively it uses those bits to represent the tonal levels in the image. For some images this can result in the irretrievable loss of highlight and/or shadow detail.
No Compression - Camera Raw files are not usually compressed, if they are, a lossless algorithm is employed. JPEG compression, even at the highest quality settings, removes a lot of data from your images which can severely limit what your are able to achieve in post-processing.
Increased Latitude - Latitude describes the exposure characteristics of film emulsions or digital sensors in terms of their ability to cope with a range of light levels. When the range of light levels (called the dynamic range) in a subject is within that capable of being recorded by the film or sensor, latitude provides an indication of the degree to which the image can be over- or underexposed while still producing acceptable results (i.e. image detail in the highlights and shadows).