It allows you to test multiple Landing Pages and see which one brings the better results. Basically the users that click on your ads will be redirected randomly on one of the 2 pages that you included in the test, and you can see from the statistics which one has a better bounce rate, goal completion or whatever metric is important to you. (A Landing Page is the page of your website where users are being redirected after they click an ad.)
A/B testing is comparing two versions of a web page to see which one performs better. You compare two web pages by showing the two variants (let's call them A and B) to similar visitors at the same time. The one that gives a better conversion rate, wins! You can write two different ad copy with similar Landing page and then you can analyze which ad copy is performing better than other. So this the way we do an A/B testing.
A/B testing in adwords is 2 or more Ad Copy and one that has a better CTR or conversion rate is winner