In corporate speak, it refers to an management or executive "pet project" that may or my not warrant the current level of attention or investment were it not for their personal support. It may mean that the executive has a personal stake in the success of the pet rock initiative and will not allow the perception of "failure", regardless of its actual merit.
Corporate peon 1: What a worthless project. Why are we still doing that?
Corporate peon 2: That's Mr. Whitmer's pet rock. There's nothing we can do about it.