Egg Moves are moves that Pokemon can "inherit" from their parents through breeding and hatching a Pokemon from an egg. There are some moves that can only be acquired from breeding. Only Pokemon in the same egg group can breed and provide an egg, and Pokemon can have either one or two Egg Groups they belong to; examples of egg groups are "Human-Like," "Monster," "Water 1", etc.
PLA Egg Type Groups List
Knowing what Egg Group your Pokemon are in is necessary to know before you can begin breeding your Pokemon. Below, you will find a complete list of all the Pokemon Egg Groups available.
How To Get Egg Moves in Pokemon LA
To get Egg Moves, you will need to breed two Pokemon together that are compatible to obtain an egg, and once hatched, the Pokemon that came from the egg, depending on its gender, will inherit moves from the parent it shares its gender with. With this method, you can have your Pokemon learn moves that they usually would not be able to.
Example of Egg Moves being passed down to the egg pokemon from bulbapedia.net