A brand positioning statement is a readable, concise version of your mission or vision statement.
Houston Chron Small Business says, A well-conceived positioning statement has four components. First, it must define the target audience -- the attitudinal and demographic description of the core group to whom you want to appeal. Second, it must delineate the frame of reference -- the category in which the brand competes. Third, it must point out the benefit, and fourth, it must give the potential consumer a reason to believe the brand will deliver on its promise.
I like to think of it more simply. A positioning statement (for a website) answers the question "what is this site about, and why should I care".
At the end of the day, answering that question is the difference between converting a customer, and losing a lead.
Ask.com recommends these as examples to emulate:
The Performance Foundry 2018 positioning statement: Performance Foundry specialises in better WordPress websites for businesses worldwide.
When you arrive on a webpage, what do you want to know? Probably you're looking for an answer to a question: who are you, and how can you help me? Following a search engine result or a link off a business card, it'll be a bit different, but that's the crux of it.
Can a random person who's never heard of you answer this question when they land on your website? If you have a good positioning statement, they should be a lot closer to an answer within five seconds. And if you have the answer to their problem, you have a new client in waiting.
Use your positioning statement on your homepage, so it's the first thing someone sees. On other pages, use it high in your sidebar or prominently on your footer, to help reinforce that brand position.
A good brand positioning statement is the heart of a marketing plan, and you could pay big bucks to a consultant to help shape it. If you're not at that stage of your business and want to keep it in house, then here's a way to get started.
These links have some other ideas about brand positioning, which could be useful.