Process A and process B are called Independent Processes if the execution/output of process A doesn't affect the execution/output of process B and vise versa. On the other hand, Cooperating Processes are those whose execution/output can affect or be affected by this of other processes.
Reasons that we might be interested in having two processes cooperating with each other are:
Cooperating processes require some type of inter-process communication, abbreviated as IPC, which is most commonly one of two types: Shared Memory systems or Message Passing systems.