Compression means that the image will never be exactly the same as it was before pixels were squeezed out and thrown away. If the compression level is low, image quality degradation is so small that you won't see it at all. But if you use high compression, images may not be as sharp or gradients as subtle, and you might even see unwanted artifacts, like specks of light. Displayed on the Web or printed as a snapshot, that image loss may be quite acceptable to you. It's when you want a high quality image, or you're making a larger print, that even the untrained eye can see the difference between compressed and uncompressed images.
Most digital cameras give users the choice of selecting the appropriate compression level.
High compression, if you want to take lots of shots, and low compression or even uncompressed, if you want better image quality. In an ideal world, your camera would make all the right compression choices for you. However, since we're not yet in a technological nirvana, use your own judgement as to what level of compression to use, according to how you intend to output or display the images you shoot.