A/B testing (also known as bucket testing or split testing) is a method used to compare two or more versions of the same page to determine which one performs better.
Let's consider an example. You have your own landing site with your service there. You improve your brand awareness, people start visiting your landing site... and nothing. Everyone is faced with this pain point: why you have low conversion rates but have a great visitor number? You can try to guess it and iterate your attempts but you can't be sure that your page performs better cause you can't measure your results. The easiest method to find out the difference between old-style copywriting and a new one is to show both examples for each half of your users and track their behavior. Let's call them A and B group. If visitors from A group with your new style of texts hit "Register" button more often it definitely performs better. And this is exactly an A/B testing.