A/B testing is a form of testing in which 2 variants, of for example a page or an advertisement, are tested against each other in order to test the conversion. Which page or which advertisement works better and converts better? Each visitor will see one of the two pages or advertisements. 50% of the visitors will see version 1 and the other 50% will see version 2. Often you will see obvious differences in the numbers and so the best converting page or ad will emerge.
The purpose of this is actually to find out which one converts best and use it on or as a sales page. A conversion actually means that a visitor takes an action for which you have set goals. Think of the goals of converting into sales, pressing a certain button, putting a product in a shopping basket or just making a transaction.