The small government is where the government tries to remain passive meaning that the citizens have more freedom to their life. This however also means that the society could also be more dangerous as people are more free to do any actions they want. Also often referred to as anarchy.
The big government is where the government tries to remain in total control on the society meaning that the citizens get less freedom to their life. This however could also lead to the society being a safer place as it will be more regulated and controlled. However the citizens will have less choices of actions. Often referred to as Dictatorship.
These two opposing ideas often clash in debating and could be a very useful concept as they are used in the context of freedom vs security where freedom represents small government and security represents big government.