If you're guessing that I like this episode because it in part features Wesley, you're right. But it's not just Wesley - Picard gets some good lines, and we get to learn about the Academy. So, without further ado...
The Enterprise arrives at Revla VII so that Wesley can take his Starfleet Academy exam. The exam isn't pass-fail, but a competition between him and the handful of other candidates. As the episode progresses, Wesley makes friends with the other candidates and even encourages them to have faith in themselves for the exam. Meanwhile, the Enterprise undergoes an investigation led by Admiral Quinn, an old friend of Picard's. Eventually the investigation turns up that Picard is awesome and there's nothing wrong with the ship. Admiral Quinn then invites Picard to be the next head of the Academy, which Picard of course turns down. Wesley faces his fear of indecision during the psych exam, and though he does well, ends up losing out to his friend that he helped during the exam. Picard tells Wesley that (shh!) he didn't get in the first time he took the test, either, and to buck up. No one leaves the Enterprise and life goes back to normal.
It was nice to see more about Starfleet Academy and the entrance exams, since normally we only hear about such things in the past tense. It helps flesh out the Star Trek universe, to say that yes, there is really an Academy that all the officers went through, and it's still there, and it's still churning out hotheaded youngsters like Riker. Normal life goes on even when the Enterprise is busy discovering Atlantis and then stealing their children back from Atlantis.
By the same token, it's nice to see that Wesley is subject to the same rules as most people even though his mother's a hot doctor and he lives on the most happening starship in Starfleet. You'd think they'd tell him that a year's experience on the USS Enterprise counts as his entrance exam, and he's in. I mean, for goodness sakes, the kid almost got killed back on Edo just because he fell on some flowers. I bet that's not the kind of thing his rival was thinking of when she told him that he was so lucky to be on the Enterprise and get real experience. But then, of course he's lucky, because some alien told Picard to stop being mean to Wesley and encourage his talents. Any way, it was good to see that other teenagers from different backgrounds had similar intelligence and potential as Wesley - especially the guy who beat him, although it's not a surprise that Wesley isn't going to be leaving the ship any time soon, so somebody had to beat him.
Oh, and, I've got to mention the hints about Wesley's father's death. Dratted hints! All we know now is that Picard had to make a tough decision and Wesley's father ended up dying. Oh, and I guess we know that Dr. Crusher doesn't hate him for it, which I had kind of already figured.
Ok, so, the other half of the episode was sort of about Picard and sort of about a vague over-arching plot that may or may not come up again in following episodes. Interesting. I'd prefer that it did, but won't be surprised if it doesn't. Apparently there's some kind of conspiracy, maybe, and maybe it's from inside the Federation and maybe it's from the outside. Heck, maybe it's Q. There's a lot of maybes, but whatever intrigue is going on is the reason that Admiral Quinn wants Picard to head the Academy.
And oh, watching Picard think about it was pretty awesome. You just know he's going to say no. Leave his starship, and do it to watch after young men and women? Leave it to head a teaching institute? No, thanks. I think Picard would die an early death with a job like that. A desk job. Ha. And, as he points out himself, Picard's not good with politics. Why should he be? He has no practice with it. Telling an alien species off is a bit different from how you get things done when your opposition is all "on your side" and supposedly "on the same page." Dealing with aliens is much more, "this is how it is," and "no, we don't want to kill you," or "no, you can't kill us." And also? If you manage to escape, you never have to see those aliens again. Picard can just tell Starfleet to put that planet on quarantine. Check it. Why would he give that up for a desk job? Ha.
The best part of the episode, though, is watching Picard tell Wesley that he didn't pass his first exam either. That's kind of like if your kid doesn't pass his driver's test the first time, except way more monumental, like, uh, space college. Space Harvard. You'll get in next time, Wesley.