Blocky colors on large pictures?

This isn't tecnically a question about an icon... but I want to make icons out of pictures like this and I can't figure out what to do about the blocky colors. I have a feeling that it might just be me, my computer, my dialup, because other people work with these pics and there's no weirdness. It's happened with me before, whenever I try to get really big hi-res pics (although sometimes hi-res works fine). Is there any way to fix it? A reason why it happens?

Thanks in advance.