Programme music (or "program music" in US English) is music for instruments which describes something or tells a story. It is the opposite of "absolute music" which is not trying to describe anything, just the sound of the piece. Programme music was very popular in the 19th century although some programme music was written earlier.
Some composers in the Renaissance and Baroque periods wrote music which described battles. Antonio Vivaldi wrote a very famous set of four concertos for violin and strings called The Four Seasons. Each of the movements describe things happening during the year's seasons, e.g. the birds singing in the spring, snowy winter days, etc.
At the start of the 1800s, Beethoven wrote a pastoral symphony, Symphony No. 6 "Pastorale", which describes the peaceful life in the countryside. This way of making music describe things became very popular with Romantic composers. Mendelssohn wrote "concert overtures" which had nothing to do with an opera but were simply short pieces of music for orchestra which told a story. Hebrides Overture, for example, describes the feel of the sea lapping into Fingal's Cave in the Scottish Inner Hebrides.
Franz Liszt made programme music very popular in his symphonic poems. Hector Berlioz's Symphonie Fantastique describes a story he made up himself about a man who has dreams about a woman he loves. The woman he loves is represented by a tune (melody) which is heard in different ways during the symphony. It is called an idée fixe (French for "fixed idea"). This way of linking a theme (tune) with a person led to Wagner's use of leitmotif in his operas in which a tune is linked to a person, event or idea. At the start of the 19th century Richard Strauss wrote several symphonic poems, often using a leitmotif to describe the person it is about. They include Don Juan, Don Quixote and Ein Heldenleben (A hero's life).