I lol'd. Too much to handle? It's not that complicated actually. Hopefully I can explain it..
Let's start with an example. Just this lv1 Ditto I caught in the wild and Nicknamed "Whore" because Ditto can breed with any Pokemon.
Stats (the normal ones you see in-game)
HP: 12
Attack: 5
Defense: 6
S. Attack: 6
S. Defense: 6
Speed: 5
EVs:
HP: 0
Attack: 0
Defense: 0
S. Attack: 0
S. Defense: 0
Speed: 0
They always start at 0. Now if you were to win a battle using Ditto, it would gain a certain number of EV points. What you get towards your stats depends on the Pokemon you defeat. I believe Machop will give you 1 EV towards Attack. You get the EV towards whatever stat that the Pokemon you defeat is highest in. I think Machop is highest in Attack. So you get 1 EV towards attack for defeating him. For every 4 EV points towards one stat, you will get an extra +1 when you level up. Let's say you level up now with 0 EV in Attack. It will just go up +1. But if you were to defeat 4 Machop and get 4 EV in Attack, when you level up from now on it will go up by +2. Basically having more EV towards a stat will increase that stat by a higher degree upon level up. In current Pokemon games, you can get up to 252 EV points towards one stat. Usually people max out EV in two stats. I maxed out my Blastoise with HP and Defense. He's a tank. Basically the more EV points you have towards a stat, the faster it will grow.
IVs
HP: 8
Attack: 0
Defense: 23
S. Attack: 30
S. Defense: 24
Speed: 14
Now we get to IVs. You cannot adjust these. They are given by "birth." Looking at these... this Pokemon would be destined to be really good in Special Attack. Since there are 0 IVs in Attack, this Pokemon is destined to be horrible in Attack. These numbers are randomized. They can go from 0-31. It's possible to have all 31 IV stats, but the chances are about 1 in 8,000 or something like that. Now let me generate this Pokemon to be lv100 just for demonstration purposes. Keeping the EV's at 0 though.
lv100 Stats (the normal ones you see in-game)
HP: 214
Attack: 101
Defense: 124
S. Attack: 144
S. Defense: 125
Speed: 103
Now you can really see how IVs come in to play. If the IV was 31 in Attack instead of 0, it would have had an attack of 132 instead of 101. Now if there was 252 EV's in Attack as well as 31 IVs it would have an attack of 195. 101 to 195 is a big difference.
To sum ALL OF THAT up.... Having high EV/IV will make your Pokemon significantly stronger than it would be otherwise.