The pace at which a piece is played can range from very slow ("largo") to unbelievably fast ("prestissimo"). Additionally, the names of symphonic movements are often given the names of their tempos. Here's a quick, short guide, from slowest to fastest.
Largo:
A realllllly sl-o-o-ow tempo. Slower than lento, slower than andante, slower than adagio. Pretty goldurned slow. Example: Dvorak's "New World Symphony," second movement.
Lento:
A broad, slow movement.
Adagio:
A slow, leisurely tempo.
Andante:
Slow and stately. Often interchangeable with "adagio."
Allegro:
A fast tempo. Used often in the first movement (the sonata) of symphonies. "Allegro con brio," the marking of Beethoven's Fifth Symphony, means "allegro with fire."
Presto:
A very, very fast tempo.
Prestissimo:
Reallyreallyreallyfast.