We called it EV training, or Effort Value training. Officially referred to by GamFreak as "base stats," a Pokémon's EV makeup affects how much each stat grows when gaining experience. When coupled with the Pokémon's natural strengths, whether it be in HP, Attack, Defense, Special Attack, Special Defense, or Speed, a properly EV trained poke quickly becomes a formidable opponent. For example, a Pokémon trained to specialize in Attack and Speed would be great at quickly sweeping opponents.
EV Break Down
A Pokémon has a maximum of 510 EVs to give out, with each specific stat able to carry a maximum of 255 EVs. Though because the number has to be divisible by 4, the preferred number to max out a stat is 252. E.g.: if you want to raise a sweeper, you would ideally allocate 252 EVs to Attack or Special Attack, 252 EVs to Speed and give 4 to a random third stat (with the two remaining left unused). Though obviously you may want something different. Obtaining specific EVs used to require defeating 100 or so of the same Pokémon over and over again, but not anymore...
First stop Victory Town...ville Victory Road! (nailed it). The addition of Super Training to this Pokémon game brought with it some interesting changes. For one, a Pokémon's EVs are more visible now than ever before. By switching to the Super Training section of the lower screen, trainers are able to see an overview of their pocket monsters' stats. While vague, the chart gives us the best look into a Pokémon's EVs than we've ever seen. Once you've chosen the Pokémon you want to EV train Super train, you may want to get rid of all its EVs at once to give it a clean start. Hitting the main punching bad until the Reset Bag appears is the easiest way to do this. Once obtained, select the Reset Bag from the list of bags by hitting the button on the bottom right. After a while of hitting the Reset Bag, your Pokémon's EVs will be wiped, allowing you to choose how much you want to allocate to each stat.
Mini Games
Once reset, it's time to pile on the effort values. To start, we recommend using a Pokémon you're not worried about screwing up the EVs just yet. The reason for this is initially we will be playing mini-games to unlock higher level ones that yield greater effort values. By hitting the lower left button, you'll access the mini-games section. At first SUper Training Lv. 1 will be the only section available, but as you play each game levels 2 and 3 will reveal themselves. Level 1 gives off +4 EVs, Level 2 +8 EVs and Level 3 gives +12. We suggest doing Level 3 during your training since the games get easier as you play them.
Other Attributes To Consider
Even though this is a guide for Super Training your Pokémon, making your 'mons formidable can go beyond EV training depending on how serious you want to get. One other thing to consider is a Pokémon's Nature. The kind of Nature your Pokémon has, Adamant, Bashful, Bold, etc., determines which stat is naturally stronger for that specific Pokémon and which will be naturally weaker. For example, if you want a strong attacker you're better off finding an Adamant or Brave version of it than other Natures. While finding specific Natures can be a pain, breeding one with a Ditto of that nature holding an Everstone may make things easier -- should you want that Nature for more than one Pokémon.
Another attribute to take into account are Individual Values. These values are still hidden like in previous versions unless you know where to look. There are IV calculators online that tip trainers off as to whether or not their Pokémon have good IVs. One of the hints can be found on a Pokémon's summary screen to the right. Phrases like "Loves to eat," or "Hates to lose" aren't just for show.
Wrap Up
Now it should be said that doing these things are definitely not necessary for completing the main campaign. The story mode of Pokémon is generally somewhat easy and X and Y continue that tradition. Though if you plan on getting into competitive battling, these are all things you'll need to pay attention to. A Pokémon with properly assigned EVs, a good Nature and the right IVs will take you far.