From Bulbapedia, the community-driven Pokémon encyclopedia.
An Egg move is a move passed down from a Pokémon breeding pair to their offspring. This can happen in one of four different ways.
Most online Pokédexes list moves from the third category as a Pokémon's Egg moves. Before breeding a Pokémon, one must consider whether to use any Egg moves in that Pokémon's moveset, and breed accordingly. To learn more than one Egg move, since they are only passed on by the father, only a father Pokémon in the appropriate Egg Group that can legitimately have all of the moves in one moveset can be used. This makes certain combinations of Egg moves impossible for certain Pokémon: e.g. Tentacruel has both Rapid Spin and Mirror Coat as available Egg moves, but no Pokémon in the Water 3 Egg Group can learn both moves so Tentacruel can't use both in the same moveset.
Sometimes to get a certain moveset onto a Pokémon, such as a Spinda with Wish and Baton Pass several steps must be taken. This is called chain breeding.
Rules of Egg move breeding
If both parents know one or more moves that their offspring could learn by leveling up, the offspring will have that move. For example, Gengar and Mismagius both know Mean Look, so their child, Misdreavus, who learns the move at level 19 will know it when it hatches.
TM and HM moves
If the male Pokémon knows a TM or HM move that the offspring can learn, the offspring will have that move. In this example, the father, Gliscor, learns X-Scissor naturally, and his child, Joltik, can learn the same move through TM81, so it will know this move upon hatching. Prior to Generation V, this was the only way to "reuse" one-of-a-kind TMs, like the ones obtained from Gym Leaders.
If the male Pokémon knows a move that the offspring can learn only by breeding. For example, if a male Dragonite knowing Outrage is bred with a female Charizard, the resulting Charmander will know Outrage.
All offspring Pokémon, in the absence of passed-down moves, will know at least one move when hatched, labeled in their level up move list as either "Start" or "--" in lieu of a level number. If these moves, together with the other Egg moves obtained in the above ways, number more than four, then the moves on top of their level up move list (with "Start" or "--") will be the ones that do not show up.
- Genderless Pokémon cannot inherit any Egg moves, as they can only be bred with Ditto, and always start with a fixed number of moves. Some of these, such as Unown and Beldum, are also incapable of learning moves via TM and HM.
- Pichu can "inherit" Volt Tackle if the female Pikachu or Raichu of the breeding pair holds the Light Ball.
- Incense-bred Pokémon often have a different Egg move list than their evolved forms.