To make breeding go the fastest you will need two of the same Pokemon that do not come from the same trainer (One yours, one traded)
Chain breeding is the process of trying to give a Pokemon an egg move that requires a Pokemon that in itself needs to learn that egg move through breeding This should help explain it better.
It is most practical if you are looking for the best egg producing results to simply have a traded ditto as it can breed with any Pokemon but will still gain a 50% chance of producing an egg.