There are generally two types of processes that run on Linux.
1) Interactive processes are those processes that are invoked by a user and can interact with the user. Vim is an example of an interactive process. Interactive processes can be classified into foreground and background processes. The foreground process is the process that you are currently interacting with, and is using the terminal as its stdin (standard input) and stdout (standard output). A background process is not interacting with the user and can be in one of two states – paused or running. 2) Daemon (day-mon) is the term used to refer to process’ that are running on the computer and provide services but do not interact with the console. Most server software is implemented as a daemon. Apache, Samba, and inn are all examples of daemons. Any process can become a daemon as long as it is run in the background, and does not interact with the user.(Source: www.2000trainers.com)

Are more detailed explanation of Linux process management can be found in the "Linux Tutorial". This tutorial contains several animations:

Animation #1 - "Reading programs from the hard disk to create processes"
Animation #2 - "Relationship between parent and child processes"
Animation #3 - "Different layers of file access"
Animation #4 - "Processes using differing areas of memory"