A webmaster is the person who looks after a website: putting the pages up, keeping them working, fixing broken links, updating the content. The '-master' part means the one in charge, the same way a postmaster runs a post office.

The word suggests one person doing everything, and that tells you its age. In the 1990s a single person really could build, design, write, and repair a whole site. Small sites and school pages often ended with 'Contact the webmaster' and an email address. Now the work is split among many roles — front-end developer, back-end developer, designer, content manager, sysadmin — so companies rarely use the title, though a small business or a club might still have one person they call the webmaster.

You may also meet it as a verb, meaning to run a site, but this is rare and sounds awkward to most people. Stick to the noun.