Your question is quite broad, so I will try to give you some background from which to build your own analysis of Touchstone. First, he is either referred to as a "clown" or a "fool." These terms may seem interchangeable to us, but to theatre-going audiences of Shakespeare's day, they were very different beasts.
A Clown was simply an actor who possessed physical skills such as tumbling and juggling and was in the play to provide moments of comedy, often physical in nature. The servants in Shakespeare's early plays -- The Two Gentlemen of Verona, The Comedy of Errors, and The Taming of th Shrew -- all serve as Clown characters. The problem for a playwright with the Clown was that he didn't really pay close attention to following the text word for word, since much of his comedy came from pratfalls and improvising lines while in performance.
Enter the Fool. Touchstone can definitely be considered to serve as a "fool" in As You Like It rather than a "clown," and it is an important distinction. Though fools existed in Shakespeare's day as jesters who served in noble households (and Touchstone is described as such in the play), in theatre the existence of the Fool as a character type was invented by Shakespeare. To keep the comic actor in line and dependent on his words (rather than ad libbing for comic effect), Shakespeare invented the witty character who accompanies the action of the play, commenting on the behaviour of others rather than getting overly involved in the dilemmas of the plot.
With the advent of this witty, language dependent player, Shakespeare also recruited different actors to play his Fools than had played the Clowns. The most famous of these Fool-players (and the one some believe that Touchstone was written for) was Robert Armin.
In As You Like It, Touchstone does accompany Rosiland and Celia to the forest, and he actually gains a love interest, Audrey. However, his relationship with Audrey, his conversations with Jaques and the other characters he meets, are all there to provide verbal humor and to illuminate the qualities and dilemmas of those upon whom the events of plot hang. Touchstone stands a bit outside the action, providing comic observance through his words of wit. This is his dramatic function as the comic Fool in the play.