It's a puzzle game.
That's basically it. There's not a lot more to it than that. There have been puzzle games that have elevated the genre, but unfortunately, this is not one of them. It's not bad, but it's not particularly good either.
Your task is to reunite numbered carriages, in order, to the train engine, by placing rails. Each puzzle has a limited number of rails to play with, so solutions cannot be simply tenable, they must be efficient. The challenge is often in ensuring the carriages arrive in the proper order (without colliding), delaying carriages 3 and 2 with a longer track. In later puzzles, this can be done with the aid (or not) of boom gates and tack switches, which which can make your final solution tick along pleasantly, like a Rube Goldberg machine.
The game is quite pretty. The cel shaded look works well, and there's a cute story about a father-son pair of pups that's told through a sequence of drip-fed, hand-drawn "photos" at the end of each level set.
Ultimately, Railbound didn't really grab me, though this is not uncommon for me with puzzle games. I found the puzzles mechanical, and frequently (but not always) joyless. They weren't always easy, but after a little trial-and-error, I would usually say, "Yep, that worked", and move on without it making a lasting impression. It efficiently killed time, but I can't say I was satisfied at the end of play sessions.
I may be holding Railbound to an unrealistic standard here. The renaissance of indie gaming that online distribution has brought has spawned some truly terrific, memorable puzzle games.
Unfortunately for Railbound, one such game was a (now discontinued) mobile game called Trainyard - another train-inspired puzzle game. It featured a similar set of mechanics, but small differences lent the game far more depth, and the final solutions would come out so aesthetically pleasing that I would watch them on loop. This was what I was hoping for. It was not what I got.