Yeah, this is an actual problem that can affect even seasoned runners when they progress upwards in distance due to a progressive loading training plan.
What is runner's toe? It's nasty. It's painful. It's subungal hemotoma, caused by repeated trauma to the toenail that leads to bleeding and discoloration. It hurts like all billy hell, and many times leads to the entire fucking toenail falling off (but hey, once that happens, there's no further pain! Winning!! Sure, it's at the cost of a heinous looking toe, but what the hell ever).
What causes it? Oh, just your toenail being slammed repeatedly into the toe box of a shoe. Or having something heavy dropped on it. It's more probable to happen when you run long distances, do downhill running, or start running again after a prolonged break.
Things you can do to avoid it? Wear proper running shoes, warm up and cool down before and after running, incorporate strength training and stretching into your workouts, cross-train, and have a formal gait analysis. And I'll tell ya, sometimes even if you do all that shit, you get it anyway.