Poker skill is the exploitation of advantages: both simple and extremely complicated ones. Exploiting advantages in game selection, venue (ring games, tournaments), bankroll, hand situations... these are all examples of poker skill.
Many people look at the "skill" in poker in a very limited and extremely unhelpful way. They think of actual hand-playing skills as the skill in poker, when those skills are merely a subset of a greater number of skills.
Poker is played for money. Money is how we keep score. But correct play is not judged by who wins the most money. Correct play is a matter of positive expectation on our actions -- and our actions include many more things than merely betting. I don't like to think in terms of "the best players" because that is basically meaningless. The best players though are the ones who play correctly. The best players are the ones who consistently get the best of it the best.
A player who could be or even should be a great winning player is not a great player if he makes losing choices. Circumstances dictate a player's ability. If the best Holdem player in the world were to walk into a cardroom every day and only play stud, that person could be a poor, losing player, even though he could be more successful than anyone else if he made other choices.
Skill is not some mysterious ability that doesn't ever exist in actual reality. Skill is only skill when it is applied. Some folks who can be great players in some situations are complete fish in others. Some of the most talented poker players are dead busted because they in fact often play poker terribly.
This is not a semantic point either. Look around a cardroom at the most successful players at every limit. Except for the influence of random luck, they are the best most, skillful players. Next look at the desperate, busted guys -- some have tremendous, but limited skills. It simply doesn't matter if they have potential to play well if they don't. They only become good players when they do play well. Playing poker terribly includes playing in the wrong games, under-bankrolled, with no sleep, blind drunk, etc.
Poker ability is simply getting the best of it. There are a lot of ways to get the best of it. Poker is more than just a bunch of cards. Poker goes on between hands in table chatter, and before games in strategic decision-making. Some of the folks who play hands well simply can't master the other poker skills (and vice versa). Reading players, making value bets, correct laydowns, inspired bluffs, all those things are about getting the best of it. But so are playing sober, choosing right games, choosing the right venues, etc. Where and how can a person get the best edges? That is skill. Getting edges. A player will not be a great player if he doesn't exploit edges where they exist.
It is 100% percent mathematical. The fact that we can't ever know or measure who gets the best of it the best doesn't mean that the cold, hard, indisputable math doesn't exist in the eyes of God if nowhere else. Getting the best of it is getting the best of it, not taking the worst of it even if you could take the best of it.
David Sklansky once wrote of two distance runners. John runs the mile in 3:50 while Harry runs it in 3:52. Harry's problem is he always runs his first half-mile in 1:45, "not knowing or caring about the fact that physics teaches a steady speed is best. And that he could therefore put together two 1:54 halves if he only changed that one simple tactic." John already knows this. Given how easy it is for Harry change his ways and if he did John couldn't win, he would call Harry the better miler. "Heart and desire is not a technicality. Realizing you should run your first half slower is."
This is an incomplete analogy. Suppose Harry is told this physics truth and he knows it to be true... but he refuses to do it! This makes Harry a dumber runner than John, it makes him always lose to John, and makes him not the one to bet on! Knowing the right thing to do doesn't count for anything if you don't do it. When it comes to skill, "realizing" doesn't matter. "Doing" matters.
People can play poker for other reasons, like ego, but correct poker playing is putting yourself in the most mathematically advantageous situation possible. This doesn't mean that sometimes you shouldn't make negative expectation moves. "Advertising" bluffs and sitting in an unfamiliar game to learn how to play can easily both be longrun positive expectation actions even if they aren't as you actually do them. These temporarily negative expectation moves are examples of the excellent application of poker skills.
Fortunately for those of us who play for money, lots of folks continue to play for other reasons, even though poker is played for units of financial value. Getting the best financial value is in no way connected with getting the most ego. There are exceptions, but in general people who play for ego end up with ego (and debts) while the people who play for money end up with money. Poker will always be a gold mine for people trying to get the gold because so many players aim for other things like ego and machismo, and give away their money while pursuing $$$-worthless goals. The poker world is littered with the carcasses of pseudo-macho, ignore-expectation-play-for-ego losers -- even though many of them have a great deal of limited skill.