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A musical tempo marking that means a piece or movement should be played quickly, lively, and cheerfully.
Der letzte Satz der Sonate muss allegro, also in einem heiteren und schnellen Tempo, gespielt werden.
The last movement of the sonata must be played allegro, that is, in a bright and fast tempo.
'Allegro' is a technical term from music and is used almost exclusively in this context. It is an instruction for musicians indicating how fast a piece should be played.
In den Noten steht, dass dieser Teil allegro gespielt werden soll.
The sheet music says that this part should be played allegro.
As an Italian loanword, 'allegro' is not declined in German. It always keeps its basic form, even when it comes before a noun.
Der erste Satz ist ein Allegro.
The first movement is an Allegro.
The word can also be used as a noun: 'das Allegro' (the Allegro). It then refers to an entire movement or piece of music composed in this fast tempo.
Das Allegro dieser Symphonie ist weltberühmt.
The Allegro of this symphony is world-famous.
fast / quick
'schnell' and 'allegro' both have to do with a high tempo. 'schnell' is the general word for movements, actions, and processes. 'allegro' is used almost only in music. It describes how a piece should be played: fast, lively, and often with a cheerful character. So in normal everyday situations, you say 'schnell', not 'allegro'. 'allegro' is more precise when you are talking about sheet music, a piece of music, or an instruction for playing.
Der zweite Teil des Stücks wird allegro gespielt.
The second part of the piece is played allegro.
Nach dem Unterricht läuft sie schnell zur Bushaltestelle.
After class, she runs quickly to the bus stop.