To all the people saying that Kopitar needs to train more in the offseason, I'm not sure at all that's the issue. Kopitar was slower this year, but that's the knee injury and not strictly a fitness issue. Recall seasons past, or watch the highlights of him playing in Sweden, and it's obvious that his physical fitness is not a big problem. He blows by defenders with his skating, and outmuscles them with his strength. Granted, Swedish league defenders are not NHL defenders, but there are no shortages of guys there who skate well and are strong. Plus, we've seen him do it to NHL players before, so it's not that Kopitar is exactly unfit.
Thinking about it more, and listening to what he was saying, I think it's more of a mental issue. Kopitar needs to go to the net. He needs to play in the middle, and not get himself stuck to the boards. You don't need to be fast to park yourself in front of the net, and on the rare occasions in this year's playoffs when he did that, he scored goals. Plus, when Kopitar goes to net, he draws defenders and opens up space for his linemates. This past playoff, he got stuck in the habit of going to the boards, the one place where he's easiest to defend. He wasn't skating well enough to make much happen on the rush; he got into the habit of playing along the boards, got tied up there, and had his space taken away; thus, he created little offense, could not sustain any pressure, and his linemates weren't particularly successful either. (Williams did very well, obviously, but a lot of his success came without Kopitar.)
Kopitar needs to relearn the habit of driving hard to the middle, of playing for and occupying the middle of the ice. When he's struggled in the past, it's because he fell back to the perimeter. Being fit is a necessary condition for his success, but it's not sufficient, because all the fitness and strength in the world won't do anything if he doesn't start coming off the boards and driving to the net on a consistent basis. And that's a mental issue. That's a habit of mind one has to cultivate and maintain.