When the Enterprise stops to repair an observation outpost, the outpost's shields are accidentally disrupted and one of the proto-Vulcan Mintakan are injured. Dr. Crusher beams the Mintakan aboard, fixes him up, and wipes his memory, but something goes wrong with the memory wipe because he remembers seeing Picard. Once returned to his people, he starts a religion revolving around "The Picard" which ultimately can only be stopped by Picard himself showing up and offering to get shot by an arrow. Before that, though, Riker and Troi try other stupid ideas that only cause more chaos.
The one thing that's disappointing about this episode are the various comments degrading religion in general. I have no problem with the premise of the episode being that a religion builds around an alien sighting. Shoot. People make their brains jump through all sorts of hoops to explain what to them is the unexplainable. That doesn't mean that Star Trek has to make it sound like all religious people base their beliefs on random weird things that happened to their predecessors. We just don't want a religion based on an accidental sighting of Picard! And there the episode gets it right - the only way to correct such a mistake is to tell the truth. If the unexplainable is explainable, explain it. Especially if you're the one who caused the misunderstanding in the first place. Even the Prime Directive agrees. (Right? It should).
It is also nice to see that the Enterprise crew tried to fix the problem without revealing themselves further. You know, like they actually care about that Prime Directive thing they all swore to follow. Plus, the episode would have been really short if Picard beamed down at the beginning to tell every one what's what. Instead we had to wait until lives were actually at stake. That's the Star Trek way!