So, a number of things can be inherited through breeding - we glossed over these earlier: moves, IVs, Nature, species, and abilities. Here's the specifics:
Only certain moves can be inherited, and it's not necessarily clear what. However, if it's a move the Pokémon would normally learn by leveling up, it can be passed down by either or both parents knowing it.
Certain Egg Moves , often only found on certain species, can be passed down by both parents - not every move is an Egg Move, keep that in mind.
Individual Values (IVs)
IVs (Individual Values) help to determine stat growth by Level 100: for each IV in a stat, you will then earn 1 point at Level 100. IVs range from 0 to 31 in all stats. Generally, it's determined by an RNG in the game if you don't hold certain items.
If the named item below is held when breeding, there's a good chance that the named stat will be inherited, and pretty much certain it will if both hold it.
- Destiny Knot: 5 random IVs
- Power Anklet: Speed
- Power Band: Special Defense
- Power Belt: Defense
- Power Bracer: Attack
- Power Lens: Special Attack
- Power Weight: Max HP
Pokémon have specific natures , which you can effectively engineer so that you get better stats (+10%). Generally, it is determined at random. However, holding an Everstone guarantees that the child gets the holder's Nature - obviously, if the parents differ in nature and both hold Everstones, it's a 50-50 crapshoot.
Previously mentioned, if two Pokémon are in the same Egg Group, then the child is of the female's species, except under specific circumstances.
In Pokémon X/Y, every Pokémon has two slots for abilities . In the named list, every final-listed ability is a Hidden Ability, unless it is the only one (which means it WILL have it). Otherwise... When it comes to the first-listed one, the child has a 80% chance of inheriting it, and 20% for the second one: first and second refer to the female parent's current Ability and the one it doesn't have, respectively.
For example, let's say you're breeding two Fennekin. If the female has Blaze, then there is an 80% chance the child will have Blaze, or 20% for Magician. Likewise, if the female Fennekin has Magician, then there is an 80% chance of the child getting Magician and 20% for Blaze.
There are special, rare abilities called Hidden Abilities - they were normally only found through the Dream World on the Global Link in B/W or some Pokémon just outright had them.
They're a bit different when it comes to inheritance in that the female or the male can know it. If the female has it, there's an as-of-yet-undetermined high chance of it being inherited. If you don't have a female with it, you can breed the male and Ditto for a chance at having it.
Normally, one of the more obvious ways to detect illegitimate Pokémon on pure observation was the Pokéball they were caught in. Since some Pokémon, such as Munchlax, are only available through breeding, you would have to be suspicious in previous generations if the Munchlax was caught in anything other than a Poké Ball.
This is different in X/Y - now the Pokéball that caught the female will be seen as having caught the child. This has a bit more of a strategic effect than you think. If you throw out a Dragonite from a Poké Ball online, your opponent could be certain it knows the Egg Move Iron Tail to counteract any Ice-types he may send it against it.
If it comes out in an Ultra Ball or the like, he/she can be more certain that you found it (or a pre-evolutionary form) in the wild and it won't know it. But since this is masked, no one knows...
The Shiny attribute of a Pokémon cannot be inherited. However, the Masuda method, which basically makes you breed with international Pokémon, allows Shinies to be almost six times more common. The specifics... Pokémon in the wild have a chance of being Shiny equal to 1 in 4,096 in this game, which is basically 0.0244%.
You can use PokéRadar/Fishing chaining to boost it up to 40 in 4,096 or so (0.976%) if you're lucky. Then again, those preferring to breed can use two Pokémon from different-nationality games (basically yours and another country's) to make the chances 1 in 1,366, close to 3 in 4,096, or about 0.0732%.
It's still rare as crap, but it's probably worth it if chaining ain't your thing.