What does "(Player name) has not rebuilt their base and is being revealed" mean?

Solution 1:

When a player no longer has any "main" buildings (Command Center / Nexus / Hatchery), this message appears. After a short time, that player's buildings, and buildings only, will be revealed to its enemies in the minimap and the main game window. Only the buildings themselves appear, you do not get vision of their surroundings.

Once that player starts rebuilding a main building the "is no longer being revealed" message appears and then you lose vision of the buildings - though a more common follow-up to the "is being revealed" message is "has left the game" :) That cycle of being-revealed / no-longer-being-revealed may repeat multiple times in the same game.

The purpose of this mechanism is to prevent an almost-defeated player from hiding a building somewhere remote in order to needlessly prolong a losing game.