There are at least 240 different types of files that can contain photos. Having said that, let's look at the 3 most common: JPEG, GIF and TIFF.
TIFF - Tag Image File Format, is raw images, just like they would come from a scanner. These tend to be huge. You can compress them. Your mac comes with the command-line program "zip" (and the companion "unzip"). It probably also has "bzip2" (don't have a Mac anymore, sorry).
Most formats, like GIF and JPEG, have built in compression. There is some small amount of "header" information, but the "body" of the data is compressed. (GIF tends to be good for when there are relatively few colors, like say a screen shot of something on your computer, whereas JPEG tends to do a better job where you have many colors, such as photos). Most photos these days are JPEG files.
Generally speaking, you can't compress files that are already compressed. You are not likely to squeeze any more space out of a JPEG or GIF.
