A process is a program that is running on your computer. This can be anything from a small background task, such as a spell-checker or system events handler to a full-blown application like Internet Explorer or Microsoft Word. All processes are composed of one or more threads.
Since most operating systems have many background tasks running, your computer is likely to have many more processes running than actual programs. For example, you may only have three programs running, but there may be twenty active processes. You can view active processes in Windows by opening the Task Manager (press Ctrl-Alt-Delete and click Task Manager). On a Mac, you can see active processes by opening Activity Monitor (in the Applications→Utilities folder).
The term "process" can also be used as a verb, which means to perform a series of operations on a set of data. For example, your computer's CPU processes information sent to it by various programs.