JPEG files are small, good quality and compatible with pretty much every peice of hardware and software in the world. JPEG files are compressed to make them easier to store or to be transferred, by this compressing the file you will lose quality depending on the level of compression.
JPEG - positives
compressed to small files, less room, quick to copy and open on any computer
negatives
lossing format, lose quality
TIFF files are larger than JPEGs because of this the files are a higher quality. TIFF files can also be saved with layers which can be created on photoshop and saved, so when you re-opened that file all the layers will still separate and you will be able to carry on and edit them.
BMP files are generally uncompressed and retain all the image information of the original copy, but this file cannot save layers..
PNG files were created for internet display, Like TIFF files they compression the file but not much so the file size will still be large, and like GIF files which PNG was created to replace can store animation information.
RAW files are used when taking an actual photo, and as the name says it saves the raw image you have just shot so during editing you can do anything to it for example: blown out highlights or dark areas can be retained as the data in those parts have been saved with some detail even though they are not visible at first. RAW files are much bigger than jpeg, you have to use special software for opening and editing RAW files, such as photoshop.
