I'm not in a 12-step program, but if I decided to go that route, I would probably use a vision I always have about "the bigger picture", be it anything. It can be broken down into various smaller compartments, though. The essence is that for me, a "higher power" is not something esoteric, not something outside of me, not an ideal, a guide... But a system I belong to, a system I am part of. A unified whole that, while it's built from elements, the entirety of it, with all the connections and relationships, is more than the jumble of the individual elements could be. It's all about the connections, cause-effect, action-reaction, interaction, how everything affects everything in a dynamic, ever-changing complex. Like in the physical world, the mind, the sciences, human relationships, and many more. It's not outside of me, just larger than me because I am a component of it, playing my own role. The effectiveness of the "power", to me, really depends mostly on how receptive I am and how willing to play my role in the system.
So in the sub-context of recovery, it could be the program and the community I am using, but I am doing my part in it and not just receiving guidance passively. I could not do it alone, but it would not affect me either without my active participation.
For those that are familiar with the concept (in different fields) of Gestalt - I think that's closest.
For me, pretty much all of mental maladies, dysfunctions, anxieties, etc have always come from a disconnection with the rest of the world, from isolation. So conversely, I definitely get a higher power from belonging and from playing my part.