What does a negative moment of inertia mean?

When we are talking about simple Ixx or Iyyvalues, then yes these will always be positive. However, when talking about moment products like Ixy, these will not necessarily be positive, mainly when holes have been cut in these cross sections.

When the holes are cut in, those moments then become negative, and due to the parallel axis theorem sometimes these negative values actually become larger than the initial value, and the moment then becomes negative.