Mleh, this one's kind of rambling, but I hope it proves interesting.
What are the things that your character "has" during a match? You have stock and percent. The match itself has time, which can affect how you play strategically. In the case of the ICs, you have a Nana. As a Peach, sometimes you have a projectile. As a recovering Link or Samus, you may or may not have your grapple available.
Playing well is determined by how these resources are used and expended. Obviously you don't want to lose stocks or gain percent, but sometimes strategically expending those resources is smart. Crouch-canceling comes to mind; SD'ing in a 2v2 match can get you back into the fight faster to help a teammate. Or having your teammate take a stock may cost you resources but give you an immediate advantage in its place.
In one of David Sirlin's articles (can't find it at the moment) he mentions that in Starcraft there are minerals, gas and units as your resources. However, there is another resource that players have, which is attention.
Where you put your attention is incredibly important. There are times where you have to be focusing on different aspects of the match, otherwise you screw up. You have to pay attention to executing this combo, then you have to pay attention to guessing this tech-chase, and so on.
You can also think of your attention placement as a strategic decision. It takes a lot of concentration to execute difficult technical maneuvers; if you believe your opponent to be weak against technical rushdown, it might be a good idea to stop thinking and start hammering him with relentless shield pressure. I try not to be extra technical so that I can instead pay attention to guessing what my opponent will do. However, one of my friends was also a mentally focused player, but had trouble dealing with really fast players. When I needed to beat him, I stopped worrying about what he would do and focused instead on having an extremely fast and tight aggressive game so he wouldn't have time to think at all.
Now for a different story! I recently started learning some Marvel vs. Capcom 2, and my friend was showing me basic combos and giving me some idea about the flow of a typical round. So, having learned only one or two useful combos, I tried playing against a different friend named Joe who was only a little better than me.
I had no idea where to put my attention. It didn't matter if I could guess when Joe was going to throw out his assist, because I didn't know what to do. I also couldn't focus on what I wanted to do, because then I was just attacking blindly and running into his stuff. It took a lot of rounds before I didn't have to consciously remember some of the game's most basic mechanics, but afterwards I immediately started landing punishes with significantly more efficiency. Of course, I'm still terrible :)
I bring that up to demonstrate a few things. First, unless you completely understand something, you will use extra attention on it. Second, because you only have so much attention to pay, if you aren't spending it in the appropriate area at the appropriate time, you will get distracted and screw up.
So let's recap. Performing unusually challenging technical stuff takes up your attention (though this differs from player to player). Trying to watch for a specific approach, or look for a particular opening takes up your attention. Figuring out what move you want to use at any moment takes up your attention. If you know exactly what the opponent will do next, and your technical game is 100% ingrained into your hands, and you always automatically know what move works best, then you don't have to pay attention at all to win. It would actually be accurate to say that you aren't paying attention to more things than other people; instead, you don't need to pay attention because you perceive those things automatically.
Assuming your brain doesn't instantly and perfectly process every detail of the match, you will have to swap your focus around a lot. It's not enough to say "I need to concentrate better," but you have to know what to concentrate on at a given point. You have to focus on watching the opening, then you swap your focus to tracking DI for your grab combo. Then you swap again to see if he'll land on a platform or bounce off, then you move over into calling his tech. However, if you know that he always techs left when he lands on the right platform of Battlefield, you can focus on spacing your tech-chase knee perfectly instead. Then you'll be paying attention to how many taunts you can get away with before they respawn.
In order to make use of this knowledge, it's incredibly important to understand your own capabilities. You need to know what you can do automatically and with great consistency, and make that the foundation of your game.
There's more though. Being able to shift your opponent's attention during a match is a valuable skill, and an important part of this game's mental battle. If your approaches are weird and unorthodox, your opponent must make a choice. They will either start putting attention on trying to understand your playstyle and mentality--which increases the likelihood that they make other mistakes--or they will ignore it, which increases the odds they will make bad decisions.
If you mix up your rhythm, the opponent can become distracted while trying to figure out your erratic movement patterns. If you alternate between rapid-fire technical rushdown and patient, turtle style defensiveness, the other guy will become preoccupied trying to figure out what on earth you're about to do next, which can make him impulsive and less attentive to things like smart positioning, good mix-ups, or even the right timing for a shffl'd n-air.
There are a million things that can shift your attention; good focus is based on knowing when, where, and why it happens and being in control of it. The first step is shutting out ALL external factors, because those have nothing to do with whether you should be shield pressuring with drill-shines or spacing cross-up back-airs. After that, it's up to you and understanding your own skillset. Know what you can do with minimal focus, and put that attention elsewhere.
I'm sorry that rambled so much, but I hope it proved interesting nonetheless. Peace.
Edit: I was really out of it when I posted this and left a few random sentences unfinished. I apologize to anybody confused by my spaced-out silliness.