German term (edited): jmd. zeigen, was eine Harke ist

to be coolest of them all, that kind of thing is meant when somebody "zeigt jemand, was eine Harke ist".

To put a person in one's place is more of a rebuke, while I understand this context to be more about showing off.

German term (edited): jemandem zeigen, was eine Harke ist

to make somebody look bad by showing them impressively how it's done/ by demonstrating one's superiority

basically to beat them at anything they are doing
to give them a good/sound thrashing

give someone a good dressing down - this is often used as English equivalent:

http://en.wiktionary.org/wiki/dressing-down

"I'll give him a dressing down, see if I don't." Mrs. Mudge's eyes snapped viciously, and she clutched the relics of the broom with a degree of energy which rendered it uncertain what sort of a dressing down she intended for her husband. — Horatio Alger, Jr., "Paul Prescott's Charge", 1865

http://en.wiktionary.org/wiki/thrashing#Noun

Noun
Singular
thrashing
Plural
thrashings

thrashing (plural thrashings)

1. action of the verb to thrash
2. a beating, especially a severe one
3. (computing) excessive paging within virtual storage
4. Dance: slam-dancing.



http://www.yourdictionary.com/thrashing

* sound: Give him a good, sound thrashing, do you hear?
* good: Give him a good, sound thrashing, do you hear?
* real: I can't find the thread but we gave this topic a real thrashing last year ( Summer?
* hard: I noticed a lot less hard disk thrashing when playing BF2 after I did this.
* regular: Despite our regular thrashing of Churchill, the rest of the season turned out to be a bit of a disappointment.

http://de.wiktionary.org/wiki/Harke

Jemandem zeigen, was eine Harke ist = jemand anderem die eigene Überlegenheit zeigen