There are two main meanings for it:
1. A person who puts winning ahead of everything, even if it brings down the quality of the game for him and/or others. He'll constantly play only what he deems are THE MOST powerful characters or use only THE MOST powerful weapons. What is deemed most powerful or effective is usually a general consensus and the Tryhard is only following the herd. He'll be playing a character in LoL or DotA not because he likes it or because he's good at it, but because he was TOLD it's the best one.
Tryharding may or may not correlate to actual winning. The term isn't about that, it's about desperation. The people it describes are desperate to win and only win and nothing else matters.
2. An insulting term roughly equivalent to "no-lifer", usually used by people to deride players who beat them. The implication here is that the only reason the "Tryhard" won a game or an engagement was because he was using overpowered game mechanics instead of playing for fun or normally.
Personally, I've found plenty of examples of the first meaning. There really are some people who really only care about winning. Not so say that I don't (I do, quite a bit), but to them it is literally the only motivation and they seem incapable of understanding why someone would play in a way that they perceive as non-optimal.
The underlined part is key here, since Tryhards are often wrong. One of the key components of tryharding is the lack of personal input. They aren't playing in a certain way because they found it to be good or fun or effective, but rather because they were TOLD that's the best way. They likely have characters or gameplay styles they like, but those are disregarded. Heck, they might even get better results with other methods, but will ignore that because they were TOLD this way is better.
And that's the sad thing about Tryharding...