JPEG - The camera processor makes decisions about colour balance, exposure, contrast, saturation, etc., then discards unnecessary inforrmation captured by the sensor and saves a "ready to print" picture in a compressed format. Most of the time it does a very good job and the compressed format saves memory space and reduces write time.
RAW - The camera records all the data captured by the sensor. The photographer then has to use a computer program to make decisions regarding colour balance, exposure, etc. This allows the photographer to custom fit the processing to the individual image and better correct errors made in camera settings. Whether the photographer does a better job than the camera depends on the skill of the photographer, the computer software used and the nature of the subject. This is more time consuming, but has the potential for better results in many circumstances.
TIFF - is a lossless file format. Each time you save a JPEG file the compression algorithm is run again and a little more data is lost. Many photographers will do some post-processing of JPEG images captured by the camera and do not want to lose any more data each time they open the file, make an adjustment and save. To avoid this they use TIFF for saving their changes. Many RAW shooters also use TIFF for the same reason. Most of us save our original JPEG or RAW shots as well for archival purposes just in case we want to go back and re-do the adjustments when we have improved software or developed more skill.