Unix is a multiuser, multitasking operating system, which means that many users can run many programs, all at the same time. It is the responsibility of the kernel to allocate CPU time to each of the running programs of a system.
Processes are what the kernel uses to handle this accounting. You can usually think of each process as a separate program that is running on the system. However, some large programs, like a web browser, may actually be comprised of many separate tasks (processes) that run simultaneously.