Theatrically speaking, it was a convention of theatre in Elizabethan England for young boys or young men to play the female roles. Because Shakespeare's company was an ensemble of actors who appeared in each of his plays, actors generally were cast in the same sorts of roles over and over again. For example, one actor specialized in playing the fools, one was most often the leading man, and there were particular actors who specialized in playing the female characters.
This practice was not perceived as "tranvestism" in Shakesperae's day. This is a 20th century concept and is meant to describe something of the sexual proclivities of the person doing the cross-dressing. For the actors in Elizabethan theatre, being a man playing a woman was simply the theatrical convention, probably not meant as a sexual statement at all. Audiences were quite used to this and didn't associate anything odd or out of character or necessarily sexual about it.
The fact that Shakespeare often gives very masculine character traits to his feminine characters (Lady Macbeth, Cleopatra, even Juliet), could definitely, however, be attributed to his complete awareness of the irony of a man pretending to be a woman onstage, and having some of his female characters decide to dress as a boy probably also satisfied his sense of theatrical irony.
Shakespeare used lots of techniques -- including a play within a play, direct reference to how "all the world's a stage" in the text of his plays, and having female characters (already played by boys) decide to go undercover dressed as a boy -- to remind the audience that the world of the play was purely theatrical and not in any way "real," though it's themes and events might hold a mirror up to nature.
So, the most immediate implication of the cross-dressing required of some of the female leads in Shakespeare's comedies is the theatrical irony of calling attention to the fact that there is really no "girl" at all onstage, and that the world of the play is completely theatrical and in no way real at all.
The British theatre company Cheek By Jowl became famous a few years ago for an all male staging of this play which they toured in Europe and the US. Seeing an actual all-male production of this play might give you the best information about the theatrical implications of cross-dressing in As You Like It.