What is meant by dressed to the T? What's a T?

a number of explanations but the most accepted comes from "dressed to go to a tea" or stated as "dressed to a tea"; however the Oxford English Dictionary takes it back at least 300 years where "to a tee" meant "exactly, properly, to a nicety"--also written as "To a T".

http://www.phrases.org.uk/meanings/to-a-t.html

The T in most "to a T" phrases is thought to stand for "Tittle".

http://www.phrases.org.uk/meanings/to-a-t.html

QUOTE:

To a T
Meaning
Exactly; properly; precisely.
.....
The letter 'T' itself, as the initial of a word.

If this is the derivation then the word in question is very likely to be 'tittle'. A tittle is a small stroke or point in writing or printing and is now best remembered via the term jot or tittle. The best reason for believing that this is the source of the 'T' is that the phrase 'to a tittle' existed in English well before 'to a T', with the same meaning; for example, in Francis Beaumont's Jacobean comedy drama The Woman Hater, 1607. we find:

Ile quote him to a tittle.

In this case, although there is no smoking gun, the 'to a tittle' derivation would probably stand up in court as 'beyond reasonable doubt'.