Expressions for tempo: 

What is tempo?: 

Musicians use the word tempo to describe the speed of the piece. Tempo is measured in beats per minute (bpm) a beat is the equivelent of a crotchet or eighth note. For example if the piece of music has a bpm of 100 that means that their are 100 crotchet beats per minute. The bpm will be displayed above the piece as a metronome mark that will also indicate if the piece is played straight or if it is swung. 

What are some expressions for tempo?:

Before the invention of the metronome, composers used various Italian, French and German phrases in order to describe the tempo of the piece. Here are some common ones.

Allegro: Quick or lively

Moderato: Moderatly 

Andante: 'Walking pace"

Adagio: Slow

Langsam: (German) Slow

Schnell: (German) Fast

Grave: (French) Slowly and solemnly

Additionally other phrases are used to indicate a change in tempo. 

Accelerando: Getting faster

Rallentando: (Rall.) Slowing down but for emphasis (e.g.  at the end of the phrase)

Ritardando: (Rit.) Slowing down, but holding back (slower)

A tempo: Return to previous tempo