The Picolo trumpet is a smaller version of the trumpet, that is also tuned an octave higher than the regular trumpet. Since the 19th century, regular trumpets have three valves. The piccolo usually has four valves. Note also that the piccolo trumpet is different from the pocket trumpet. A pocket trumpet has the same tonal range as a regular trumpet; it is just built differently (to be smaller).
A piccolo trumpet has another characteristic tone, which can easily be distinguished from that of a regular trumpet.
The piccolo was developed in the first quarter of the 20th century, mostly by Julius Kosleck. Kosleck used it to make it easier to play baroque music. Note however, that at the time of Johann Sebastian Bach, the trumpets had no valves; these were added in the 19th century.
Piccolo trumpets could not establish themselves in Jazz music, but they are often used to play classical trumpet.
The trumpet is a "noble instrument"; it is often used to play high-pitched notes. Such notes are easier to play with a Piccolo. Because of its construction, the piccolo cannot play the first octave of the classical trumpet.
Like the regular trumpet, the piccolo is a transposing instrument.