If you have a place that's all your own, somewhere real or in cyberspace that has your name all over it — literally or figuratively — it's your domain. And if you have something you really excel at, that is your domain too. You own it.
A domain used to mean only land owned by wealthy people, such as lords in the 15th century, but modern usage is much wider, or has a broader domain in the English language. On the Internet, a domain is a space with a specific address, but a domain can also have a physical address, like a home. It can be a specialty, too, as in, "The main domain of the art school was sculpture," or "She was so good at math that algebra became her domain."