Adjective, and also a noun. A white-tie event is the most formal kind of social occasion there is in Western dress custom. Men must wear a white bow tie, a black tailcoat (a jacket cut short in front with two long 'tails' at the back), a white waistcoat and a stiff white shirt; women wear a long evening gown. "White tie" written on an invitation is an instruction, not a description.

Because it sits at the very top of the formality ladder, the word is really a measuring stick. One step down is black-tie (black bow tie, dinner jacket / tuxedo) — far more common, and what most people mean by 'formal'. So when someone says "it's white-tie", they are saying: this is grander than a wedding, grander than a company dinner. In real life almost nobody attends one: state banquets, royal occasions, some old university balls, the Nobel Prize ceremony, a few charity balls in New York. Many English speakers have never been to a single white-tie event in their lives.

Used as a noun too: "He was in white tie." And people stretch it as a joke or an exaggeration — "this isn't a white-tie affair, just come as you are" — meaning don't worry, it's casual. Note the hyphen appears before a noun (a white-tie dinner) but usually not after the verb (the dinner is white tie).