A/B testing is when you run a test by creating multiple versions of a page, each with its own URL. When users try to access the original URL, you redirect some of them to each of the variation URLs and then compare users’ behaviour to see which page is most effective.
Multivariate testing is when you use software to change differents parts of your website on the fly. You can test changes to multiple parts of a page—say, the heading, a photo, and the ‘Add to Cart’ button—and the software will show variations of each of these sections to users in different combinations and then statistically analyze which variations are the most effective. Only one URL is involved; the variations are inserted dynamically on the page.
Official Google Webmaster Central Blog: Website testing