A process is independent if it cannot affect other other process or be affected by it. Any process that does not share data with others is independent. Otherwise the process is cooperating. Cooperation is done to provide information sharing, computational speedups, modularity and convenience. To allow cooperation there should be some mechanism for communication (called IPC: Inter-Process Comm.) and to synchronize their actions.
The best way to see the cooperation is by seeing an example of consumer-producer. Producer produces and consumer consumes. Producer puts its production in a buffer and consumer picks it from the buffer. (Buffer could be provided by OS using IPC)