Admittedly, I know next to nothing about the real Vincent VanGogh, but this episode is regarded (rightfully) as a really good one involving the Doctor, Amy, and Vincent VanGogh working out a problem together.
Also, Bill Nighy has an uncredited role as an art professor at a museum.
See, the Doctor is trying to cheer Amy up over the death of Rory. True, Amy has no memory of Rory, like, at all, so she isn’t sure why she needs cheering up, but here we are. Visiting a VanGogh exhibit at a museum seems like a nice way to go until the Doctor notes some weird things about the painting, including one that might be…him? There’s a doctor in one that tried to treat VanGogh the year before he died after all, but there’s something in this church that caught the Doctor’s eye, so if taking Amy to see the work of VanGogh is one way to cheer her up over something she doesn’t remember, then taking her to meet the actual guy might be even better.
Well, it might be if VanGogh didn’t have severe depression, though later he gets happier and that could suggest manic-depression. Again, I don’t know if VanGogh suffered from either, but that’s how he’s portrayed. He’s also portrayed as a sad drunk in a town where everyone thinks he’s insane. Then again, he can see some kind of invisible monster.
The Doctor can’t without special equipment, but it turns out to be a mostly invisible alien, blind and somewhat prone to hostility, that his best efforts to return to where it was supposed to be end tragically when the creature accidentally spears itself on VanGogh’s easel, and by then VanGogh felt mostly bad for it. As depressed as he is, the Doctor does the thing that makes the episode: he takes VanGogh to 2010 to see the museum exhibit and hear Nighy’s professor call VanGogh one of the greatest men or artists to have ever lived, lifting the man’s spirits in the most beautiful way possible. He and Amy return the man to his own time, and Amy figures he didn’t kill himself then so there must be more art in the present/future.
And there isn’t because mental illness doesn’t work that way. There are some small changes to the artwork, including one dedicated to Amy, and that’s it. VanGogh still killed himself on the same date. It’s a sad moment, but one made better by knowing that, for one brief, shining moment, the Doctor showed VanGogh that yes, he will matter a great deal and be appreciated for all time.
Besides, VanGogh recognized Amy’s grief over Rory even when she didn’t. There’s something going on there. But all the grieving young women and invisible monsters are just a side thing when there’s a moment of pure joy on an artist’s face. There’s a good reason that people remember that moment if nothing else.