EVs are effort values, or the additional stat boosts gained from battle, vitamins, ect. Every 4 EVs will raise a stat by 1 at level 100, with each pokemon able to gain 510 EVs total and 255 per stat. 252 is the point you'll max the stat out at so you can max out 2 stats and dump 4 EVs into another. Every pokemon defeated will give 1-3 EVs to pokemon who gain experience from it and the species determines which stats those are in. The intended results of this system is to make every pokemon more unique by growing from their experience, like practicing something to get better at it.
IVs are individual values, the individual pokemon's natural talent for the stat. They range from 0-31 and increase the stat at a 1:1 ratio instead of EVs 1:4. Prior to bottle caps they could not be changed so breeding for the spread you want is primarily how it's done.
Egg moves are moves a pokemon can only learn if they inherit it from a parent and may require jumping through hoops to get a male parent with the move in the same egg group as the species to breed with a female to get offspring with the move before you even bother with IVs or natures. For example back in gen 4 I planned a team with a typhlosion using thunderpunch and extrasensory, so I had to take my typhlosion from Colosseum in gen 3 over to emerald to teach it thunderpunch via tutor before sending it to gen 4 because I only had diamond at the time, get a fresh smeargle to teach extrasensory to by using it in a double battle against an npc so it could sketch the move from my other pokemon, then find someone with hgss to trade them over to and breed them together then send me my pokemon and eggs back because hgss is when they added it to typhlosion's egg move pool.
Natures are like a personality trait that makes a pokemon good at one stat and bad at another, +-10 with natures that boost and nerf the same stat being neutral. Like IVs they originally couldn't be changed but gen 8 introduced mints for that.
