tl;dr – Be excited about finding abandoned structures. Be potentially excited about reinforced structures.
A structure will be in one of four states: Vulnerable, Low Power, Reinforced, or Abandoned. An existing structure may also have a “Core Absent” state combined with its active status.
A Vulnerable structure is powered and may be attacked. It has two reinforcemnt periods: one after shields are gone, and one after armor. To destroy the structure, you shoot through shields, wait out the reinforcement period, shoot through armor, wait out the reinforcement period, then shoot through hull to destroy the structure.
For a Low Power structure, there is no reinforcement between shields and armor. Shoot through shields and armor, wait out the reinforcement period, then shoot through hull to destroy the structure. Many structure owners keep their structures in a Low Power state until they need to use services or defend the structure. Low Power is thus not a reliable indicator of an opportunity for content.
After a week in Low Power, a structure enters Abandoned state. An abandoned structure has no reinforcement period, and can be destroyed in a single session. An abandoned structure is either bait (opportunity for content) or a potential killmail.
A Repairing structure has exited the Reinforced state, and is self-repairing in order to return to its default (Vulnerable) state. Self-Repair will may be paused by applying sufficient damage to the structure.
Core Absent: Services are offline. Reinforcement is the same as a structure with a core. Tethering, Repairing, and Refitting are disabled.
A Reinforced structure is sometimes interesting. Some people reinforce their own structures in order to control their own repair timers. These are usually uninteresting. If it is reinforced by a third party, there is an opportunity to kill the defending or attacking fleets, or to potentially sneak in to steal loot.
Learn more about Vulnerability States
Learn more about Abandoned Structures