FocusFollowsMouse is a paradigm for activating windows in a GUI: the active window (the one that will receive text if you type, for example) is defined not by which window is frontmost, but by which window the mouse pointer is over. If you look at the BeOS Focus Follows Mouse example, you will get a good idea:

Many Linux/Unix hackers love this; it is highly useful when dealing with multiple TerminalEmulator windows. MicrosoftWindows and AppleMacintosh users tend to find it terribly alien and confusing. (But MicrosoftWindows users who like it can get it by downloading the TweakUI powertoy and enabling the XMouse mode.)

There are several variations on this focus policy. A common one is known as SloppyFocus: in contrast to strict FocusFollowsMouse mode, where moving the mouse over the root window (outside of all application windows) causes no window to be focused, SloppyFocus means that the last focused window retains focus until the mouse pointer enters another window.

FocusFollowsMouse is often combined with AutoRaise, where the focused window is raised after some delay (eg. 750ms). AutoRaise always involves a delay, as you obviously don’t want windows to come to the front just because the mouse pointer happened to travel across them.