You could say 'red' eighteen times, or you could tell the person drawing for you 'fill in the next 18 squares red'. By doing that you're saving yourself a lot of breath. And that's what compression does. It looks for patterns in the file and instead of storing eighteen pixels of red, it stores the number '18' and the pixel colour 'red'. Lossy' means simply, that information is lost in the compression process.
All images can get away with losing at least one pixel.
Well, GIFs get a bit muddled up by this. JPEGs are smarter, and they take small variations of colour into account. A JPEG will take two shades of blue in adjacent pixels that are very similar, and discard one of them, making both pixels the same colour, and thus much more compressible. You can control how lenient you want the JPEGs to be. This is where the concept of JPEG 'quality' comes in.