It was the play by the Viennese playwright that Beethoven wrote the overture for, not the Shakespeare version of the story. The story on which the overture is based:
The Roman General Coriolanus is banished from Rome after he throws a hissy fit over the citizens renouncing his bid to be elected counsel of Rome. In revenge, he goes over to the side of the enemies of Rome and plans to sack the city. He lays siege to the city and refuses to grant amnesty to his own people. In desperation, his wife and mother go to him and plead with him to spare his family. He settles in favor of his family which makes him a traitor to his allies, the enemies of Rome. In Shakespeare's play, Coriolanus' allies kill him while in the Collin play he commits suicide by falling on his sword.
Beethoven wrote only one opera, Fidelio, and it cost him much in labor and time. He never again wrote for the opera theater, but that doesn't mean his music couldn't be dramatic. This overture shows that while Beethoven may not have been a natural composer for dramatic opera, he could write pure music that could convey drama without the use of any words. It was this kind of overture that lead to the symphonic poems of Liszt and others. It would not be a stretch at all to say that this overture could be called a symphonic poem, and it is a very good example of how Beethoven inspired the composers of the Romantic era.
The following video of Carlos Kleiber conducting the overture shows how orchestral conducting is just as much an art as a science. Kleiber translates the mood of the music through his actions, and the orchestra responds. The end of the work shows how much the audience was swept up by the music, for whether they were hypnotized, stunned or perhaps equal measures of both, the applause does not start until the music had long since stopped. That is the greatest tribute an audience can give a performer, prolonged silence before the applause begins.