Take a look at Accelgor's egg moves (link is here).
Here is what I understand:
The Pokémon in the "Breeding" row, if the father, will pass down any compatible moves to the egg. Upon reaching level one, the baby already knows these moves.
I am going to use the move Baton Pass as an example in the next case. If the female Accelgor is with a male Scolipede (found in the "evolution" row), the baby Shelmet will learn Baton Pass upon evolution.
The "Level Up" row is what is troubling me. Does the baby Pokémon just have to learn the move through level up or TM/HMs?
Okay see, the Level up row isn't for the baby but for the parent. The list is just trying to tell you what compatible parent learns Baton Pass by level up, so you can breed it onto something else.
I hope this was helpful :)