It indicates that the music should be played with more and more energy, tempo, and enthusiasm as it progresses. It's essentially a directive to build the excitement and intensity of the piece.
Here are some other ways to interpret "allagrando":
* Accelerando: This is a similar term, meaning "increasing the tempo gradually". Often, "allagrando" implies a more nuanced, expressive acceleration than simply speeding up the tempo.
* Con Brio: This term means "with vigor" or "with spirit" and adds to the sense of energetic joy implied by "allagrando".
* Allegro: This term simply means "fast" or "lively". While not identical, "allagrando" adds a sense of increasing energy that "allegro" doesn't necessarily imply.
In essence, "allagrando" is a musical instruction to gradually inject more joy, vivacity, and intensity into the performance.