Something I think is important, mainly because I think it's the reason why I win more games than I lose, is adaptability.
The first, basic step in being good at boardgames is being able to get on top of, and not be confused by, the rules. But just because you know all the rules doesn't mean you're out of the woods yet! In my experience, a lot of players, having comprehended the rules, will locate what they think is a strong strategy and then repeatedly play that strategy. And at first this will probably pay off.
A good boardgame, though, doesn't have a completely dominant strategy. Any strategy should fall when met with an appropriately strong counter-strategy. A bad player, when their strategy starts getting repeatedly thwarted, may blame bad luck for the sudden downturn in their fortunes. (Actually, let me add this to my list of prime indicators of boardgaming talent: never blaming bad luck for a loss. Always looking back for a way you could have turned the game in your favour is a much better sign.)
A great boardgames player not only quickly understands what is likely to be a strong strategy in a game, he is also able to see numerous other strong or potentially strong strategies at once. When he loses, he will be able to understand what weaknesses of his strategy permitted it to be undermined; he will refactor his strategy accordingly or try out a new one in the next game.
A really strong player can see his strategy starting to be undermined as it happens and be able to switch to a different strategy mid-stream. When you have a counter-strategy planned, or can quickly create one, for any possible counter-strategy to your strategy adopted by your opponent, then you are what I'd call truly "adaptable". And I'm a little bit scared about the possibility of you joining my group and beating me lots!