What exactly does webmastering entail?

Putting new text and images on your site, handling domain name registration and hosting needs, adding and removing email accounts, and troubleshooting the website as necessary.

My last webmaster didn't give me passwords to my site. What's your policy on that?

It's your data. Freelance Digital documents all passwords and passes the documentation on to you--including what hosting company you're set up with, what's it's capable of, your domain name registration information, email accounts, database info, and more.