A time signature tells every player in the band how many beats land in each bar and which note gets counted as one beat. Learn to read one at a glance and you can sit in on almost any song — rock, jazz, waltz, or shuffle — and know exactly where the pulse lives.
4/4 is the time signature you'll play more than any other. Count four beats to a bar with the quarter note as your beat, and that's the whole rule. Rock, pop, blues, funk, and country all default to it, which is why every drummer learns to lock into 4/4 before anything else.
3/4 time drops one beat from the bar, and that missing beat is what gives waltz time its lean. Count '1 2 3, 1 2 3' and you'll feel the music circle rather than march — it never quite lands flat the way 4/4 does.
6/8 packs six eighth notes into the bar, split into two groups of three. Count all six while you're learning it, but once it settles into your hands you'll feel only two big pulses, each rolling through three subdivisions — a compound meter that grooves very differently from straight 4/4.
12/8 gives you twelve eighth notes per bar, grouped into four sets of three. You still feel four big beats, exactly like 4/4, but each one rolls through three notes instead of splitting evenly in two. Count it '1 2 3, 2 2 3, 3 2 3, 4 2 3' and the snare lands where it always does: on the head of the second and fourth group.

4/4 time means there are 4 beats per measure and a quarter note gets one beat. It is the most common time signature in rock, pop, and jazz. A standard rock drum beat with the snare on beats 2 and 4 is in 4/4 time.
3/4 time has three beats per bar instead of four, giving music a waltz-like feel. On drums the snare typically falls on beat 2 or beats 2 and 3. It is heard in songs like 'Manic Depression' by Jimi Hendrix.
6/8 time has six eighth-note beats per bar, grouped into two sets of three. It creates a flowing, compound feel common in blues shuffles and ballads. At faster tempos it often sounds like a two-beat feel.
Both can feel like 'three', but 3/4 is a simple meter (three quarter-note beats per bar) while 6/8 is a compound meter (six eighth-note beats grouped as two sets of three). At slow tempos they sound similar; at faster tempos, 6/8 feels like a driving two-beat pulse.
12/8 time has twelve eighth-note counts per bar, grouped into four sets of three. You feel four big beats like 4/4, but each one rolls through three notes instead of two. The kick usually lands on counts 1 and 7 and the snare backbeat on 4 and 10. Slow blues and 1950s ballads are the classic examples.
Both group eighth notes in threes. A 6/8 bar holds two groups and feels like two big pulses; a 12/8 bar holds four groups and feels like four, so it maps onto a 4/4 backbeat with the snare on the second and fourth group. Playing a 12/8 pattern is much like playing two bars of 6/8 back to back.
The top number (numerator) in a time signature tells you how many beats are in each measure. For example, 4/4 has 4 beats per measure and 3/4 has 3 beats per measure.
The bottom number (denominator) in a time signature tells you which note value equals one beat. A 4 means a quarter note gets one beat; an 8 means an eighth note gets one beat.