It's right there in the Meme question. It means just deleting a tag. With fire.
Meme: burninated
Origin: Possibly Jeff Atwood / Strongbad: Trogdor the Burninator
Cultural Height: 2010 - 2011
Background: Used in reference to deleting a tag from the system.
See Also: The official burninated dragon, Trogdor the Video Game.
In all seriousness, here's what usually happens:
A tag, when it's burninated, is removed from all questions that carry this tag. The entire history of the tag is wiped out, with no trace of the tag existing in revision histories. This will just remove the tag from the system, but it can easily be re-created by users with the privilege to.
If a tag is really bad, and chances are it'll be recreated soon, then it can be blacklisted. Only few tags are blacklisted, but there are many good examples, such as homework on Stack Overflow, or the pc tag on Super User, which are both Meta tagsMeta tags and shouldn't exist.
To get a tag blacklisted, asking on the site's Meta is a good choice. This is nothing moderators can do—in fact moderators can't delete tags either—so it'll require community consensus and a developer to do that.