A/B testing is a tool or technique offered by Google to verify that, which version of your website is working fine. ie, you have a web page and some images , call to action functionality, forms and contents and so. If you think to make changes in few areas of the same web page and want to see the experimental results, then this A/B testing is useful. It will give you a clear idea about which part of the web page the visitors are spend time at max and where at min time and so. By this we can get clear idea about the changes we need to implement in the web page and reduce bounce rate as well.
To be honest A/B testing has little to nothing to do with SEO at all. A/B testing is so you can server 2 different pages to users and get stats for conversions for each, example you think moving a enquiry button will help conversions but not sure. You would setup an A/B test one serving it on the old position one serving it in the new position and see from the stats which is converting better. This theory can be used for so many things where you think your going to improve useability and conversions. Things simple as colour of a certain button, changing size, location. Maybe you have a few layout ideas for a whole page, the list goes on.