I agree that the word is overused, but personally I usually use it to joke around. So when I want to sound dumb I say sumtin like ''MINDGAMEZ SON!'' or ''SNAPZ! I GOT OUTMINDGAMED!''
When I talk more seriously, I tend to use the terms that you'll see in standard fighters, like fakeouts and mixups. A few explanations for newbies here, but there's plenty of players that could do a better explanation than me:
A fakeout is a move that is used to bait your opponent into making something that puts you into an advantageous position. In smash, a good example of a commonly used fakout is dashdancing, and that PC vs M2K video shows this: the repeated dashdances make M2K whiff a grab. But dashdancing is like the simplest of all fakeouts, it can be sumtin more complicated, like a SHLing Falco that will attract a Fox Nair, so the Falco can use his own Nair to counter Fox's Nair right after that.
Another kind of Fakeout or bait maneuver doesn't simply involve a specific move, but can also involve overall tactics. Camping is a good example of this, good camping spots are spots that limits your opponent's attack options, and when you camp, you can force an opponent into putting himself in a risky position. Watch out though, he might also ACT like he's in a risky position... hehehe
Kinda like Wobbles said, mixups simply consist of varying between attack patterns in order to make your opponent chose the wrong answer to your attack. It's basically like playing rock paper scissors against your opponent. For example, you can mix between a grab or a dsmash right after jabbing your opponent, and your opponent will fail if he tries to spotdodge a dsmash or shield a grab.
That's mindgames for ya... also sumtimes playing smart is not using mindgames, because playing smart is simply using a cheap move that will work all the time in the current situation cause there is not answer to it, like a Peach downsmashing a defending opponent that is low on shield. The better characters in the game require less mindgames because they can get away with plenty of stuff without being punished (like Marth/Sheik/Peach that can space their aerials to avoid shieldgrabs, while Fox/Falco can shine right after their aerials).
Finally, like Brookman said, a very important part of the game is learning to avoid the bad situations, the traps that your opponent sets up to you. A bad Fox will simply try to reflect turnips and block Peach's float cancelled Fairs, so he will get ***** in the end. A good Fox will rather run away and laser spam, or keep the pressure with his own tactics and combos.
So to conclude I would say that mindgames do exist and are important. But they are less important then what ppl think. Ppl saying stuff like ''get more mindgamez'' is inaceptable.