Pokemon ev training questions?

I am confused about ev training. What does it mean when someone says this? 252 Atk / 4 Def / 252 Spe Does this mean to battle 252 pokemon that give out attack 1 attack evs, 4 pokemon that give 1 defense ev, and 252 pokemon that give out 1 special attack ev? What do each of the numbers mean/represent? Do the... show more I am confused about ev training.
What does it mean when someone says this?
252 Atk / 4 Def / 252 Spe

Does this mean to battle 252 pokemon that give out attack 1 attack evs, 4 pokemon that give 1 defense ev, and 252 pokemon that give out 1 special attack ev? What do each of the numbers mean/represent? Do the numbers mean that you must obtain 252 evs for attack, 4 evs for defense, and 252 evs for special attack?

From what I know, to raise a stat by 1 requires 4 evs. So, if you get 252 evs for a particular stat (let's say attack), then does that mean that you can add 63 more points to the pokemon's attack stat compared to a pokemon who wasn't ev trained in the attack stat?

I have one more question.
252 Atk / 4 Def / 252 Spe

In the above, there is a 4 before the defense stat. Why would you only want to get 4 evs in the defense stat? Wouldn't that just raise the defense stat by 1 (because 1 stat = 4 evs) ? Would getting 1 more defense stat point make that big a difference?

So basically, I just want to know what the numbers represent.

Oh and one more question.

You know how when a pokemon uses a stat changing move such as swords dance? It says that the pokemon's attack is raised "sharply". What does that even mean? Whenever I use that move during a battle, I check to see my pokemon's stats to see if my attack was actually boosted but its stats remain the same. By how many points does the attack of a pokemon go up by if the pokemon uses swords dance (and other stat changing moves)?

Sorry for the length. I'm a total noob in pokemon so help me out here :)

Thanks for your time!
Update: Thank you @Iggy and @Tennyson :) @Iggy, thanks for your detailed answer! It must have taken you a long time to write that. Thank you for your time! Your information was very helpful :) @Tennyson, as for the spe, lol I think you're right! It means speed. oops! So one "stage" is twice as much as the... show more Thank you @Iggy and @Tennyson :)

@Iggy, thanks for your detailed answer! It must have taken you a long time to write that. Thank you for your time! Your information was very helpful :)

@Tennyson, as for the spe, lol I think you're right! It means speed. oops! So one "stage" is twice as much as the original stat? and two "stages" is four times as much as the original stat? wow! that's powerful! Thanks for the info! Great answer!
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