Overture (sinfonia in Italian and Vorspiel in German) is the term for an opening instrumental music piece. It sometimes is an independent piece, which makes the overture a general opening piece for full concert. In this sense it is usually called concert overture. Most of these were composed during the Romantic Period (19th century).
Yet usually an overture is the first part of a full composition, so it can be considered the opening of a large musical work. Overtures are mostly seen in opera, ballet, and concerts but sometimes in stage music as well. Composers often used overtures to set a particular mood or atmosphere for the rest of the piece.
Through the ages overtures have seen different shapes. The oldest overtures were known as sinfonies. These 17th century music pieces were canzone-like works: unaccompanied vocal introductions, most likely with multiple voices, also known as madrigals.
In the second half of the 17th century a new type emerged. It started in Northern Italy (particularly Venice) but later on spread to France, which gave its name to the new vogue in classical music. The so-called French overture was a slow, solemn and quite homophonic start, full of punctuated (i.e. clearly separated) rhythms, usually followed by fugal, melodic allegros. These polyphonic allegros might be closed by a short, slow part which could easily be a copy of the overture.
Shortly after, around 1700, the Naples region in southern Italy developed another variety of overture. This was later called the Italian overture. It is characterized by an allegro start with powerful instrumental soli, a cheerful vocal middle piece and a festive ending which can best be described as dansant in classical music terms. This overture developed itself during the 18th century to become the most popular current of opening pieces. It's worth noting, adds tdent, that when Haydn's symphonies were played in England in the late 18th century, they were called 'overtures'.
Whereas the Italian overture was a strict composition in the beginning, the 19th century witnessed it becoming more unrestrained. Especially composers of lighter works preferred medleys or mixes of styles.
The possibly most famous independent overture is Tchaikovsky's 1812 Overture. Other composers well-known for their overtures include Ludwig van Beethoven, Giuseppe Verdi, and Hector Berlioz.