The open field system was a system where all the people of some village or other group would work the land in common. In other words, there would not be one parcel of land that belonged to Person A and another that belonged to Person B. The whole area belonged to the group (the village, the manor) in common.
The people of the village would get together, usually each year, and decide who would farm which parts of the land. The land was divided up into little strips and each family would work some certain number of strips. Their strips of land would not be right next to each other -- they'd be scattered around so no one got all the good land or all the bad land.