A process is a program that is being executed. When you start a program in Windows, Windows accepts it and allocates some processor time and memory to the process. When you close the program, the process is terminated and the resources- processor and memory- are handed back to Windows.
Processes are similar to the applications tab, which displays the currently running applications. The Processes tab displays both the processes running in the foreground (the open applications) and the services that are running in the background. A service is an executable file that runs in the background and is not designed for user input. An example is smss.exe, which takes care of the user session: when you enter your credentials and logon to Windows, smss.exe launches csrss.exe and sets the system variables. Except for Windows developers, no user plays with these services, and many users are not even aware that these services are running in their computers.
Note that, many malware applications hide themselves from the Process view or some of them have similar names which are indistinguishable from the real processes. Such as the service.exe: this is actually a Trojan, resembling the system process services.exe. If you have any doubts about the process you see in this tab, make a search on the Internet and check if it is a valid service.
In the Processes tab, you can end the process or process tree of the running applications, change their priority (priority can be Low, Below Normal, Normal, Above Normal, High, and Realtime) and set their affinity (select which processor cores the process or service can use) in multicore processor systems. If you do not know what you are doing, do not play with the priority or affinity settings.