Time Signature indicates how to
count a piece of
music. This is extremely important, for music is timed
sound and
silence.
And the musician is his own clock
The top number tells how many are counted; the bottom number tells of what.
Time Signature also indicates the emphasis of the piece, which can only be figured out by counting.
The first beat in the bar--the down beat--is always the most emphatic, loudest, or accented. In 2/4, the second beat--the up beat--is, of course, the lessor accented, or weak beat.
In 3/4 time, waltz time, the down beat is accented, and beats 2 abd 3 are weak beats.
In 4/4 time, the pattern is strong beat, weak beat, medium weak beat, weak beat.
In 6/8 time--6 beats of an eighth note each--the pattern is strong weak weak, medium weak weak. Alternatively, one could conceive 6/8 time as being 2 beats composed of 3 eighth notes each, instead of the usual 2 eighth notes to each beat.
This is why time signatures with 8 on the bottom are called compound and not simple as time signatures with 4 on the bottom are.
For more on counting, see metronome.