An impromptu is a short, single movement, instrumental piece of music, composed to sound as if it has been improvised. It nearly always refers to a piano piece, although impromptus have been written for the violin, guitar etc.,
The term was coined in the first quarter of the 19th century, with pieces by two now ignored composers titled as such. The first impromptus of note were written by Franz Schubert in 1827, though published (and named) between 1827 and 1859. Chopin and Schumann were other composers of notable impromptus during the first decades of the Romantic era and Gabriel Faure and others have written them since.
In normal conversation, impromptu means without planning, preparation or forethought.
“Oxford Companion to Music”
“The Grove Concise Dictionary of Music”