Strip the attributions away and the Emperor does a specific job in a reading, and it is narrower than "power".
The dominant sense is structure: boundaries, rules, the framework that makes work possible, and the willingness to be the one who decides. Where the Empress provides, the Emperor defines. Readers who work psychologically often take him as the internalised father, the capacity for self-governance, or the part of a person that can say no and mean it. Readers who work practically take him more literally, as an institution, a contract, a boss, or the fact that a situation is governed by rules that will not bend for the querent.
The critical readings are equally standard and worth naming, because a card of authority in a divinatory system is not automatically a good card. Rigidity, control exercised past its usefulness, an order maintained because changing it would cost face, and domination are all within range. Waite lists them as reversed meanings. Marseille-derived practice, which largely does not turn cards, reads them from position and neighbours, an Emperor falling in the position of an obstacle is an obstacle, upright or not.
One further nuance: in the older French pattern he is shown in profile, seeing only one side, and some readers make deliberate use of that. It is a modest observation about a woodblock convention rather than a hidden doctrine, but it is the kind of detail that reading from the actual card rewards and reading from a correspondence table does not.