'Try-hard' is a term used by people who lose at a game and don't want to own up to their loss. Such people take the game more seriously than the people they're referring to as 'try-hards' or 'no-lifes', but choose not to put forth the necessary time and effort to get better at the game, instead choosing to blame their defeats on better players. An excellent example is people who complain about an opponent's choice of character in a fighting game, such as the Marvel vs. Capcom 3 online player base who will insult you heavily if you use Dante, Wolverine, Gouki, Wesker, Phoenix, or Sentinel. They accuse Dante/Wolverine/Gouki/Wesker/Phoenix/Sentinel players of not caring about fun or wanting to ruin other peoples' fun, but the irony of this statement is that the objector is so closed-minded that the only definition of 'fun' that they acknowledge is their own. It never occurs to these people that perhaps employing provably effective tactics, progressing as a player, and learning more about the game is fun to some people.
tl;dr edition: If someone calls you a 'try-hard', then that person takes the game more seriously than you do, despite being worse at it, and is so obsessed with himself that the only opinion he acknowledges is his own.