Using the newest and best methods, machines, or knowledge that exist right now. If a hospital has state-of-the-art equipment, nobody anywhere has better equipment — this is the top of what people can build today. It is almost always used as a compliment, and it is almost always about technology, machines, buildings, or ways of doing skilled work. You would not use it about a person, a story, or a feeling. Two small things about the shape. When it sits in front of a noun, it takes hyphens: a state-of-the-art laboratory. When it comes after the verb, most writers drop them: the laboratory is state of the art. Also notice that it is stuck in the present. Something built in 1990 was state-of-the-art in 1990, but calling it state-of-the-art now would be wrong, and English speakers enjoy that joke — "state-of-the-art, if you mean 1995". Though actually, in advertising the phrase has been used so often that many people now hear it as noise. A company selling you a phone will say state-of-the-art about a small change. So it is strong in a report or a news story, and weak in an advertisement. There is also a plainer noun use underneath it: the state of the art means the level that a whole field has reached, as in "the state of the art in cancer treatment" — that one is neutral, not praise.