Daycare -
This pokémon always helps the younger ones. When grinding for levels, you must have The Daycare pokémon help.
i.e: Prinplup is your daycare, when grinding, you throw the pokémon out first, then swap it for Prinplup so he can easily defeat the pokémon, and help the other gain the level.
Mayor -
This pokémon is the lead party member, most likely the one with powers, and is also the one who gets a few privileges. (Can still use berries until the sixth gym). This pokémon has to be caught before the second gym. Before it is caught, any pokémon that is hurt can not be healed through the pokémon centre.
Shop keeper -
Makes sure every pokémon gets a fair amount of items. This one also gets small privileges. (berries until fourth gym). Until this pokémon is caught, pokémon get as many item usages as they like, this one must be caught before the third gym.
Adviser -
Helps the mayor make decisions. Need stock be caught before the third gym. With this pokémon in the party. This pokémon may also have powers. Nothing particular changes.
Messenger -
Highly recommended this one has powers. The messenger allows more then six pokémon to be caught, and for them to be changed at anytime, however the mayor can not be changed. This has to be caught before sixth gym.
Citizen -
This has no real job, and you can have as many as you want, this merely a filler for the gaps.