A power user is one whom make extensive use of keyboard shortcuts, rather than using the mouse to perform actions such as closing a window or saving a document, for example.
An example of a typical power user operation is to hold down the key combination ⌘⌥O (Command Option O) when opening a folder or application program to close all open windows. This particular keyboard shortcut is generally employed by power users running older versions of System Software as it is somewhat redundant in Mac OS X, where the contents of a new directory are displayed in the same window. Having said that, the shortcut does still work in the aforementioned system.
Another example of a power user operation is the converse of the previous; by holding down ⌘⌥W, all currently open windows are closed. The same effect can be achieved by Option-clicking on any of the open windows' Close box. Once again, both of these functions have been preserved in OS X, but are rarely used.