The definition of webmaster has changed quite a bit in the last 15 or so years. It used to be somebody that runs a website, knows a bit of html etc.
However now I think the definition (although it is mainly opinions, not set in stone) consists of:
- In charge of a website's daily progress. They may have a boss and they may have their own team (unlike before where generally less people would work on a website together)
- Knows and uses tools and languages such as FTP, HTML, CSS, JS, CMS software etc.
- Delegates the work around the team
- The person who is contacted in regards to the website
Some people even argue that webmaster is a defunct position, however it is still on many job titles.
Basically, a webmaster is a manager with skills based on website development, design and content management. They do not need to be a master at any one of these, more of a "Jack Of All Trades Master Of Management" kind of thing.
I hope that helps, it was my first answer on this site!