Compression is mostly about problems with storage. If everyone tried to upload a half-dozen 15-25meg images, that could be 10Tb of storage. Jpeg compression can typically achieve a 10:1 ratio. That's a lot of storage savings.
Jpeg is a lossy compression algorithm -- meaning a lot of detail (that your eye usually can't see anyway), gets thrown away. Re-saving a compressed image will eventually make it blurry and lose most details. That's why you usually want to keep your originals unedited.
But image type/format is mostly a problem with compatibility -- some browsers might support viewing bmp images, but its generally not recommended for web content. Not all browsers and platforms will support it.