Well, ill try to explain. There are pokemon abilities that have an effect outside of battle, when the pokemon that has it is on the first slot. One of them is synchronize. With that ability, the chances that you find a wild pokemon with the same nature as the pokemon with synchronize increases a lot. So thats why people get synchronizers with different natures, so they can get pokemon with the nature they need. I hope its clear, if you need anything else just tell me :D