Pokémon X & Y super training ?

[SERIOUSLY THOUGH*]

So my love and I got Pokémon X & Y, but haven't played Pokémon in many generations.
We've discovered this thing called super training that seems to increase some points (EVs).

I have no idea what an EV is and what this Super Training actually does. For example I do the HP training but my HP doesn't go up +4 like it says.

Can someone give me a super-simple explanation as to what EVs are and what Super Training actually does ?

Thank you !!