The English here should be marked "informal", I think.
The dictionary definition (e.g. Merriam-Webster online) differs slightly from the German given here: "to plead guilty to a lesser charge in order to avoid standing trial for a more serious one".
The German here sounds like what I did when I was ticketed by the police at the age of 18 in California for a misdemeanor:
I received a notice in the mail advising me of the date scheduled for a court hearing, and giving me the option of paying a fine of $140 instead of appearing in court. Advised by someone more experienced than I, I went to court simply to answer the charge by saying Yup, I'm guilty. The result: I was fined $25.
"Copping a plea," on the other hand, involves pleading guilty to something **less serious** than what you were charged with.