What is musical time?

As far as I can recall from music theory lectures in choir three or so years ago, musicians sometimes use the word “time” in the context of, say, “3 4 time.” Ah! That’s called the time signature. It goes, I think, between the symbol indicating which clef a staff represents and the key signature in written music. The time signature consists of two stacked numbers. The top number is the number of beats per measure, and I had the bottom number explained to me as what each beat counts for, but I didn’t fully understand the concept when I originally learned it. Anyways, time signature is what I think of when I think of the concept of musical time.