"Try Hard" as an insult is usually referring to the fact that people whom it's directed at go out of their way to get any slight advantage they can via exploiting mechanics/item builds/talents and what not instead of actually having fun and learning how to play what they find fun to the extent of people whom they are trying to get the advantage over.
I rarely use this term due to the fact that I don't normally insult people, but there have been a few occasions when I have come across people whom "Try Hard" would be an accurate description of them:
TF2 - I mained Sniper, I had 200+ hours of Sniper alone (Also 80-150 hours of all other classes) I had gotten very good at the game, whenever I killed one of these "Try Hards" they'd opt for 1 of 2 options; Using the same class as me (They think the class is overpowered rather than me actually knowing how to use it) or they pick the counter class for me and use items specifically designed to kill me rather than to help their team. This has had some game-ending results of the entire enemy team picking Sniper to try (Often failing) to kill me while my team wins the game.
WoW - In Battlegrounds I hold my own, I do some capping, defending and the occasional bit of killing (If there's nothing else to be doing due to flags being held and waiting for a co-ordinated strike or something) often times I try and kill Rogues when I can since I know how much they can mess with key players on my team. This usually annoys them and on a few occasions I get the 2-3 Rogues on the enemy team going around as a group ONLY targeting me and all hitting at the same time. Again this tends to leave their team at a disadvantageous position (They're playing 2-3 down while my team only has me not participating) and the rest of my team normally wins.
These are the only times I've come across people whom I'd call "Try Hards", they try hard at getting revenge usually to the detriment of their team.
Edit:
SmashLovesTitanQuest said:
DasDestroyer said:
The way I see it used and use it in Dota 2 is to insult people who do every little thing to win, rather than just playing for fun. Don't get me wrong, everyone wants to win, but when you pick the easiest character, use the easiest build on that character and then use the easiest pub strategy you're crossing a line.
And who would be the easiest hero with the easiest build that is actually worth anything against semi-experienced players?
OT: Only time I've heard it in DOTA 2 is when my team buys invis detection items against invis heros. Hilarious.
Ever heard any of the following:
GG then AM
Anti-Mage pickers!
I've heard it a few times in pubs and jokingly in some Competitive games, due to the fact he can farm up pretty fast and then just roll over most heroes.