What does a 4/4 time signature mean, and how is 3/4 different from 6/8?
4/4 means four quarter-note beats per bar. 3/4 and 6/8 both hold six eighths, but group them 3+3 versus 2+2+2: different feels.
The top number says how many beats each bar has; the bottom says which note length counts as one beat. 4/4 means count "1-2-3-4" and repeat: the rhythm of most pop, rock and hip-hop.
3/4 is the waltz count, "1-2-3". 6/8 also fits six quick notes in a bar, but you feel it as two big lopsided beats, like a rowing or galloping rhythm.
A time signature declares the bar’s size and its counting unit. 4/4 (four quarter notes) is so standard it is written C, for common time. 2/4 marches, 3/4 waltzes.
The 3/4 versus 6/8 puzzle: both contain six eighth notes, but 3/4 groups them as three beats of two (ONE-and TWO-and THREE-and) while 6/8 groups two beats of three (ONE-two-three FOUR-five-six). Same arithmetic, different pulse: that grouping is called simple versus compound meter.
You hear the difference in the accents: a waltz leans on each of three beats; a 6/8 jig swings between two.
Meter is a perceptual hierarchy, not just arithmetic: listeners infer beats and groupings from accent patterns, and the signature is the notation of that inference. That is why identical note streams can be renotated in different meters and feel different when performed with different accents.
Compound meters (6/8, 9/8, 12/8) use a dotted-quarter beat that divides into three; simple meters divide the beat into two. Beyond these live asymmetric meters (5/4, 7/8) grouping beats unevenly (2+3, 2+2+3), the spice of Balkan music and progressive rock.
Ear training for meter is its own skill: the trainer’s meter-identification mode plays grooves and asks 2, 3 or 4, which is the aural half of what the written signature encodes.