JPEG is a "lossy" file format, which means the files can be much smaller than "lossless" formats such as TIFF. However, the smaller file size is at the expense of image quality.
When you save a JPEG file, you have a slider to control the "quality". Decreasing the quality will throw away some information about the image which will make it look worse, but this will also make the file size smaller. The JPEG file format is designed to throw away first the information which the eye is not very sensitive to, so for higher quality JPEGs you can often barely tell the difference.
Note that even if the quality is set to maximum, the image quality will be very slightly degraded. Even though this may be imperceptible if you just save the image once, the quality losses will be multiplied each time you load and save the image. This means you should use TIFF files if you intend to make multiple changes to an image in different sessions or using different programs.
Also note that when you save a JPEG file with a low quality, the information is lost at that point so you cannot simply load back in the same JPEG file and save it out again with higher quality to improve the image.