Are you talking about an audition for acting or theatre? Or televsion/film?
Monologues are just bits where one person talks out loud for a while, in theatre usually alone and directed to the audience, or talking to themself for the audience's benefit, but especially in film and TV there could be other characters about as listeners as well, depends on the situation.
Think of it as an impassioned speech, usually a pivotal moment or revelation and pick one that can display the range of what you want/need to show for this audition. You need to memorise and say/act all the words, and they'll be looking for how you express the point the particular monologue is designed to achieve, through appropriate tone, expressions and movements (or lack thereof) and you rpresence.
Try here for some examples of movie ones to look through, there's heaps...
http://www.whysanity.net/monos/ It'll help you realise that there are lots of monologues around in TV as well, and you can pick one that suits what you're auditioning for. I'm not sure they'd want you to make up your own, unless the audition is testing how you'd react on the spot to things (eg presenting, live/impro)?
For theatrical monologues most traditional/famous ones come from Shakespeare, Hamlet's full "To Be or Not Be" speech, Lady Macbeth's "out damned spot" speech, Juliet's chat at the end of R&J, Falstaff's comedy monologues in the Henry plays. In high school I tried one from Henry IV on stage with poor results - forgot the words, substituted my own version of the point he was meant to be getting across and ended up on a week's detention....
So Shakespeare may be biting off more than you can chew, and may not be relevant to the audition, depending on what it's for. You'll find more monologues in modern theatre, try looking at Harold Pinter, Arthur Miller, Neil Simon, maybe David Williamson, or any known musical, anything that has had a decent shelf life on the West End or Broadway.
And break a leg!
