A wireframe is about functionality. It can be a really simple sketch that demonstrates what sort of things you can do in your design. For example, a wireframe of a website will show the navigation, the main buttons, the columns, the placing of different elements. You can think of it as a bluprint for a website.
A mockup is a realistic representation of what the product will look like, in this case a website. The final result can look exactly like the mockup, or be a variation of it after version revisions. While some people prefer to draw the mockups using graphic software, others do it straight in HTML/CSS.