"I will meet you at the train."
Translation:Mi renkontos vin ĉe la trajno.
That is two different things though, maybe only one of them were going with the train and the other was just there to say goodbye, would be quite inconvenient to meet in the train then if it suddenly were to leave, wouldn't it? At the train on the other hand means that they're at the train station, at the train at least one of them is going to travel with, but not inside it.
I'm a native English speaker, and I interpreted this sentence to mean 'at the train', or more accurately, 'at the train station, on the platform'. Ĉe means something like 'at the home of' or 'at the place of', and the home/place of the train is the train station. In (or on) the train would be 'en la trajno'.
Ok, here is my explanation from what I've picked up so far (bear in mind I'm only an intermediate learner!):
"Je" is a bit too non-specific when you're talking about going to someone's house or to a particular place like a train. "Je" can take the place of literally any other preposition, so it's correct here, but non-specific. "Je la trajno" could mean at the train, behind the train, on the train, towards the train, next to the train ... etc. "Ĉe" is the preposition that's usually used when you want to indicate physical proximity.
There's no real literal correlation for ĉe into English, which is why it feels weird to English speakers. And there are tonnes of different uses for ĉe (the vortaro entry is the longest I've seen of any Esperanto word), so there's no single translation that's going to work in every situation. In most situations it's "at" as in "near there" or "thereabouts" referring to a physical location, but it can also mean "in [the work of]" or "at [the house of], or "at [about this time]"., or even "by/holding [that person's body part]" as in "Mi kondukis lin ĉe la nazo" - I led him by the nose". But mostly, it means a spatial location, proximity to something "ĉe la trajno" = at/near/by the train.
I picked "at the place/home of" because that is one of the senses in which it's used, especially when referring to people, but sometimes also when referring to objects. (And I find it a helpful way to think about ĉe in order to remind me of the spatial thing and to distinguish it from other Esperanto words that could mean 'at' depending on the context). It's very similar to the French word chez. You can say "ĉe mi" to mean "my place", in the same way you'd say "chez moi" in French. "Ni iras ĉe mi" = We are going to my place. "Mi renkontis lin ĉe vi" = I met him at your house.
Here is an article that's quite helpful. It goes over some of the more common ways you can use "ĉe", and it's much clearer than I am :) :