For storing your images with no loss in quality (if this is what you wanted to do) I recommend .png. You can make the size smaller than .bmp and the image will still be 100% perfect.
A longer explanation:
Not compressed. Not made smaller. If we are dealing with Images then I believe .bmp is the only (or at least the most 'common') uncompressed format available. Not recommended for nearly any use these days. To make a metaphore we could say that if we wanted to leave a blanket uncompressed, we would do nothing to the blanket and just spread it out like normal.
File has been made smaller. Can be one of two general styles of compression: Lossless or lossy. Both make the file smaller but in different ways. Lossy generally makes the file much smaller than lossless but loses information about the original. Lossy compression is used with media files much more often than lossless.
Does not lose any of the original information. The original uncompressed file can be reassembled from this. If we are talking about images the most common format is .png. If it's just generic files the most common is .zip. To continue the blanket metaphore: if we wanted to compress the blanket in a lossless way we would fold it a few times so it is smaller.
Loses information about the original to save space. Images and music and video are commonly compressed in a lossy way. Information about the original file is irreversibly lost. In music for instance when compressing in a lossy manner we might lose the very high or the very low notes on the assumption that most of us wouldn't hear them anyway. For music .mp3 is the most common, and for images .jpg/.jpeg (same thing) is most common. For video, the file extension doesn't represent the way it was compressed -- the file type is just a 'container' for video and audio media. A few common methods of video compression are divx (not used these days) xvid (falling out of favor but still used) and h264 (new and gaining favor) with .avi being the most common container. You cannot use lossy compression on non-media files; it will break them because all of the information is needed. An example of lossy 'compression' of the blanket could be cutting the edges of the blanket until it fits on your bed perfectly, then folding it up.