It means that someone caught you doing something wrong, and you admit it. I couldn’t find where it came from, Chuck, but it must be akin to “cop a plea”. According to the Online Etymology Dictionary, the word “cop” originates from the word caper, which means to seize, or Latin capere, to take.

“It’s a fair cop, but society’s to blame.”
“All right, we’ll arrest them too.”
— Monty Python’s Flying Circus, Church Police

Well, I know a lot of people quote that. :)
But generally it means someone has caught you fairly and you are admitting fault. As in:

“It’s a decent, impartial cop who has found me guilty.”

I’m not sure how the phrase originated, unless it was the Python boys themselves, I wouldn’t put it past them and I couldn’t find any information on the origin online. You can see the bit here. Skip to about 1:45 if you’re feeling impatient. :)

<3 Monty Python / Hopefully, this American Girl answered you satisfactorily.

@asmonet, good answer, but it appears that the term “copper” for a policeman dates back to the mid 1800s as a slang term, and to be ‘copped” or nabbed by the police, goes back that far.

@AP: Good info, I didn’t even think to look into the word cop itself because of how commonplace it is. I went diggin’ just for that phrase only, it’s 6:30AM and I haven’t slept yet – I’m not working at full capacity. Thanks for adding that. it was an interesting article. :)

I found this http://idioms.thefreedictionary.com/It’s+a+fair+cop and this, http://www.urbandictionary.com/define.php?term=fair+cop .

The word cop also comes from an abbreviation for “constable on patrol”