In classical music, the term program music (sometimes spelled programme) refers to music that seeks to describe something or someone through suggestive means. The opposite of this is absolute music, which is music written simply for its musical value. For example, the ballet Swan Lake by Peter Tchaikovsky is program music because it tells the story that is being danced on stage. On the other hand, most music of the Classical Period is considered absolute because it lacks an explicit message.
Often, composers would literally write an actual program to go with their music. For example, Berlioz wrote out the story being told in his Symphonie Fantastique so that listeners could understand what was going on (see this page for more information on the Symphonie Fantastique.) Other times, a composer might give you a clue as to the meaning of a piece by giving it a suggestive title; for example, there's "The Sea" by Claude Debussy.
Program music has been around for quite a while; Antonio Vivaldi wrote "The Four Seasons" around 1725, and there are even earlier examples. However, the big boom in program music occured during the Romantic Period. The attitude of the time was strongly geared towards literary expression, which went almost hand-in-hand with program music.
While program music enjoyed much popularity during this time, it
did not play as big a part in chamber music as in other kinds of
music. This is because the role of chamber of music was generally
to express intimate emotions and thoughts, while the role of
program music was to convey a message or story to the listener.
Even then, there are several examples of programmatic chamber
music. Perhaps the most famous is Bedrich Smetana's first string
quartet (subtitled "From My Life"), which describes a different
episode from his life in each movement.