Exploits are "strategies" that were not intended by the game designer and completely nullify strategies that were intended by the game designer.
This is my favorite definition offered so far.
So for example, sensor boats. I considered them an exploit because they invalidated a lot of other intended mechanics.
1) Starbase Sensors: Sensor Boats were much stronger.
2) Explore Ships: Sensor Boats were much stronger and could scout quicker.
3) Pirates: Sensor Boats invalidated pirates. They couldn't spawn near your territory once you had sensor sight, and you could see them from so far away away that pirates were never a threat.
4) Sensors on regular ships: Sensor boats were a much more efficient use of space/cost. There was no point to putting a few sensors on regular ships.
So that to me is an exploit.