What is a time signature in music?

The time signature determines how strong versus weak pulses are performed in a piece of music or song. 

In 4/4 or common time the first beat is the strongest followed by weaker beats on two, three, and four. This gives the music an even feel that works well in pop and jazz.

In 3/4 time, a strong beat is followed by two weak beats. This rhythm has a round feeling that works well for waltz and lullabies.

Each time signature has its own unique character that the composer or songwriter will use to shape the feeling of a music composition.