Definition
Alternative form of to a T.
How People Actually Use It
To the greatest degree or extent; extremely, completely, or utterly.
"I know it takes me a long time getting ready, but nothing feels better than being dressed to the teeth for a night out on the town. Everyone in the bar was armed to the teeth, so we felt a little bit nervous sitting down for a drink in there. I have to say, I'm fed up to the teeth with all the people littering on campus!"
Source: Urban Dictionary