Tempo means the speed at which a piece of music should be played.

As with many other musical terms, Italian words are used to describe different tempos of music.

Adagio - a slow tempo (other words for slow are lento and largo)
Andante - performed at a walking pace
Moderato - played at a medium tempo
Allegro - a quick and lively tempo (another common word for fast is vivace)

The tempo is written above the first bar on a piece of sheet music.

Sometimes a metronome mark is used with the beats per minute (BPM) written down.

Writing the term for the tempo and the BPM gives the musician reading the music a very clear idea of how it should be played.

An andante symbol showing 90 beats per minute tempo

The image above shows the BPM (in this case 90 BPM) as well as the term andante which describes the tempo.