Fig.: to be very well dressed, fashionable and with particular care to details. To be dressed perfectly for the situation

For his first job interview Bob had to give up his usual shorts and T-shirt. He was dressed to a T in his blue suite and white shirt and he really looked very handsome

Per il suo primo colloquio di lavoro, Bob ha dovuto rinunciare ai suoi soliti calzoncini e T-shirt: si è vestito di tutto punto, si è presentato in giacca e cravatta e stava benissimo

At our company's annual dinner, I'll be sitting at our President's table and I cannot show up in my business attire. I need to be dressed to a T, so I need to go visit some trendy boutiques!

Alla cena annuale dell'azienda sarò seduta al tavolo del nostro Presidente e non posso certo presentarmi con il mio abbigliamento da ufficio. Devo vestirmi di tutto punto e soprattutto molto elegante, perciò devo andare a visitare qualche boutique alla moda!

The origin of this idiom is uncertain. One possibility is that the phrase is short for “dressed for a tea”, which dates back to the Victorian era, when high tea was a formal affair, meaning that all “proper” people dressed appropriately.
Another theory suggests that "T" refers to the letter's use in the phrase "to the teeth", which means to the maximum degree.
Yet another one claims that it refers to the expression “to a tittle”, where a tittle is the tiny dot on the letters "i" or "j"; meaning that every detail has been taken care of.