If you have a website, you probably want to constantly change appearance and behavior of website to increase some important metrics: revenue, conversion rate, happiness of users, etc.
To figure out what changes will help you to move toward your goal you can use different sources of information. You can read marketing research papers, you can use your own user experience to make decisions, and you can ask end users about their feelings. All this can help, but you will not have solid quantitative analysis about what approaches are better, and what is significance of the change.
A/B testing (also known as multivariate testing) is more scientific, more pragmatic, experimental approach.