The time signature is the two stacked numbers at the beginning of a piece of music. The top number tells us how many beats or counts per measure, and the bottom number tells us what kind of note receives one beat or count.

4/4 time is the most commonly used signature in most styles of music. In 4/4 time, there are four beats per measure, and each beat receives a quarter note. That means that in 4/4 time, we count "1,2,3,4" for each measure. 4/4 time is also called "common" time, and can be represented as a letter "C" at the beginning of a piece of music.

Cut time is represented by a letter "C" with a vertical line drawn through it, much like a "cent" sign. In cut time, the notes are written as though it has four beats per measure, but the music has a pulse that sounds like two beats per measure. Cut time is often used for pieces written in 4/4 that are intended to be played fast.

2/4 time is two beats per measure, and the quarter note gets one beat. Though not used in popular music very often, there are many classical piano pieces in 2/4 time.

3/4 time is also known as "waltz" time. It has 3 beats per measure, a quarter note gets one beat. 3/4 is probably the second most common time signature in piano literature.

5/4 time is more unusual, with 5 beats per measure. Two popular examples are "Take Five," the Dave Brubeck jazz classic; and the TV show theme "Mission Impossible."

Other signatures where the quarter note receives one beat included 6/4, 7/4, 9/4 ,etc. These are much less commonly used.

6/8 time has six beats per measure, and an eighth note receives one beat. In jazz music it is used for a "jazz waltz" feel.

12/8 time is more often used as a variation of the 4/4 time signature. There are four strong beats per measure, but each beat has a triplet feel.
Count 12/8: "1-and-a, 2-and-a, 3-and-a, 4-and-a"

Other eighth note based signatures include 3/8, 5/8, 7/8, 9/8, 11/8 etc. These are much less commonly used.