Allegro as an adverb describes the speed at which music should be played. The composer indicated that this section should be taken allegro.
Pro Tip 2/3
Mood Expression
Allegro often implies a cheerful or brisk mood in music, not just speed. Even though it's fast, make sure the allegro section feels joyful.
Pro Tip 3/3
Not Always Fastest
Allegro is fast but it's not the fastest tempo; that would be prestissimo. She played the allegro briskly, yet it was slower than the final prestissimo.