When saving a JPEG file, you are often prompted for the image quality to use. You might be tempted to use Medium, or even Low, with the idea that you can make the file a lot smaller that way. Well, it's true. The file is a lot smaller. But the problem arises from HOW the file is made smaller - the program throws away information about the picture! JPEG is known as a "lossy" file format - meaning that you lose information about the picture anytime you use JPEG compression on it. If used carefully, JPEG compression can be a great way to save some space, and make your images smaller for download.
But what if you want to edit them again later? Will you lose MORE information when you save it again? YES. This can build up to a lot of compression artifacts. What's a compression artifact? Well, here's an example.
Compare the image on the right to the one on the left. They are both saved as JPEG images, but the one on the left was saved with much higher quality settings. Normally, you won't see the artifacts visible in the right image right away, but over multiple saves, the artifacts will add up. Pay attention to the edges of the leaves and the petals. Notice how the colors go funny there. Also notice how the colors in the petals are blocky. These are normal examples of JPEG artifacts.
If you save the image with higher quality, the artifacts are virtually invisible. That in and of itself is a good reason to use higher image quality.
Something to keep in mind is that if you do a lot of work with your pictures, you will want to save them in a different image format - a lossless image format. Some common formats are Windows Bitmap (BMP), Tagged Image File Format (TIF or TIFF), and more advanced formats like Photoshop (PSD) and the GIMP XCF format. Saving in the lossless format means that you won't lose any information when you save the file, so you don't have to worry about artifacts building up in your photo. When you're ready to put it online, or share it with someone, saving it as a high quality JPEG won't damage it too much.