It's the first Federation exploration of the Selcundi Drema Sector (or Quadrant, if you prefer, which I DON'T. I prefer a quadrant to be one fourth of something. Like the galaxy. Or, even better, a pie.)
Picard's not much for small animals, but he loves to ride a horse.
Troi's people are not famously great riders, as they 'get too caught up in the shifting passions of the beast'.
"I would have thought the shifting passions of this beast would be far more terrifying." says Picard (of people).
Terrifying is the word of the day: the planets around here are falling to pieces. Riker puts Wes in charge of this investigation, and orders him to lead his first team. Possibly to pad out the story.
Ensign Davies enjoys disintegrating rocks and second guessing Wes. Rather than do five hours of work during a two month survey, Davies deftly weasels out of it. You think he'd do it out of boredom alone. But with a confidence boost from Riker, Wes makes it an order and Davies complies. Thrills galore in interpersonal dynamics! Whee!
Data happens across a little space girl with the equivalent of a ham radio set and breaks the Prime Directive to reassure her while her planet falls to ruin. Data petitions Picard to help save Drema IV. Little Sarjenka is sad and asks for help. So, against the rules, they do.
Dilithium is doing hinkey things to rocks, and a spate of technobabble is the answer!
"Right, sir. I'll just be standing over here dozing off," says O'Brien, expressing his opinion on Data's unlawful beam-down to warn Sarjenka. Data beams the glittery orange glam rock kid back, too, for a wildly unauthorized field trip.
Trying to minimize the cultural contamination, Picard has Pulaski erase Sarjenka's memory of these events. Which Data also subverts by giving her an inexplicable Elanian singer stone.
(I hope it's worth it if her people burn her as a witch.)
"Remembrance and regrets. They, too, are a part of friendship," muses Picard.
"Pen Pals" puts a lot of emphasis on how the Prime Directive ties these people's hands for simply wanting to be decent. Also, no offence, but saving this world could've been done without anyone seeing them at all. How is it breaking the directive if they never know you were there?