I think what it means (no pun intended) from a very technical point of view (though this may not be an exact definition) is that “mean” time is opposed to sidereal time. For example, a sidereal day is not “exactly” 24 hours, and “sidereal” Noon would vary from “mean” Noon in the same time zone because in a sidereal timing system “Noon” would be when the Sun is directly overhead—regardless of what the clock says.
So “mean” time groups a geographic band of varying longitudes (based on geographic features of Earth and political boundaries) and groups them together in a “Mean” timing system, so that we can set clocks similarly in various places and work by this collectively agreed-upon “mean” time.
For a more extreme example, China, as large as it is, is contained in a single time zone. So “noon” (meaning 12:00 PM by the clock) may be sometime in the afternoon in Shanghai (by a westerner’s “feeling” of what time it should be), and mid-morning in western China (by the same reckoning).
If this makes any sense…