In the digital world, compression is an incredible (and complex) thing. Basically, here's how it works:

If you took a picture of the sky during a bright sunny day, it would be this big, blue rectangle. If you saved this on your computer as, say, a .bmp, the file size would be huge (just for sake of reference, let's say, 500k). That's because with an uncompressed file, your computer has a record of every single pixel. So, basically, the code would be this in English:
Blue square, blue square, blue square, light blue square, blue square, blue square, ad infinitum, ad nauseam.

Compression, such as a .jpg file, works off the realization that things would be a lot easier if you combined sections of code. So, in English it would say something like:
Big blue rectangle.

Naturally, the second is smaller (again, just for reference, 10k).

How does this work for video and audio? I'm not really sure, but the principle is roughly the same.

So, what about "lossless" compression? Well, as the name would imply, if you do a lossless compression, you will not notice a difference in quality. This is compared to a "lossy" compression, where you will notice that not all the information is there.

Compression and you: If you listen to digital music, you probably hear compressed sound all the time in .mp3 or .acc files (but only your music buff friends will swear there is a difference). If you watch DVDs, you see compression. Even that really good looking major motion picture was compressed from beautiful 35mm film negatives down to 720x300 pixels in something akin to an mpeg 2 format. If you watch TV, the quality is likely to be even much lower.

The moral of the story: When used with care, most people will not even notice you have compressed your files.