You log in on the Gravatar website. You tell them your email address. You pick a nice avatar (or supply a little jpg yourself). The gravatar website links your avatar to your email address. That's all.
When you register on other websites, almost always you have to supply an email address. Then that website can ask Gravatar what avatar is linked to that particular email address. And the website can then display that avatar.
I got an avatar automatically when I registered here. Surprise. Because a few years ago I registered the email address I use for gaming. Still works.
The administrator has disabled public write access.