Full of life, fun, and energy — used for a party, a place, a time, or the people in it. If you say "a swinging party", you mean everyone is having a great time: music, dancing, noise, nobody sitting in the corner looking at their phone. If you say "swinging London" or "the swinging sixties", you mean a time when a city felt young and free and exciting.

Here is the honest part. This meaning of the word belongs to the 1960s. It was very popular then, and it has never really stopped sounding like the 1960s. So when people use it today, they are often half-joking, or they are talking about that time on purpose. An older person might say it straight. A younger person saying "what a swinging party" is usually being funny, the way you might use an old song. It is not wrong to say — it just carries a date on it, the way clothes do.

You should also know that the same word has a second life. "Swinging" is also the name for married couples swapping partners for sex — that came from swing dancing, where you changed partner after each dance. Because of that, "a swinging couple" means something quite specific, and not "a fun couple". The two meanings almost never get confused in real sentences, because the first one describes places and times (a party, a club, an era) and the second one describes people. But it is worth knowing so that no one surprises you.

And of course the plain meaning is always there too: "swinging" is just the -ing form of the verb "swing" — her arms were swinging, the door was swinging open.