It's an instance of the execution of a program.

          A program is recorded on a mass storage device and remains inactive so long as its execution is not launched. Once the program is started, this execution is called a process.

          One has to understand that several instances of the same process can be launched independantly. Each instance is another process. For example you can open a new window of your browser, that will be a new instance of the execution of the software of your browser.

          Some programs allow only one instance of their execution for obvious reasons. Example: The program of connection to Internet. You only need one connection (unless you want to make your Internet service provider rich...) If you try to start a new instance of that program some message or other will tell you you are already connected and will ask you if you want to disconnect.

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