These drop every time you kill a mob that is worth experience or honour (or would be if you weren't level capped) while on the quest Test Your Strength. Collect 250 of these and turn in to earn ten Darkmoon Prize Ticket and 250 Darkmoon Faire reputation. The trophies do drop even while in a raid group.
This quest can be completed only once a month. It is picked up and turned in to Kerri Hicks who is located on the Darkmoon Faire island. As such, it can only be started or ended during Faire week.