I don't know how long this feature is available - but I am a bit confused because I don't see why this feature was added - when it is not useful for anything in game, at least in my opinion.
And of course, in the matter of case, there is something what is quite strange in departures board - times of arrivals and departures. That trains need some time for load/unload is right. But really it is strange that some times are static and some ones are changing up or down - as vehicle is getting to be close to chosen (observed) station. In this it seems like ... if some trains start journey delayed and delay is erased - and some trains start journey at right time - and delay is gained.
Departure Board shows the estimated time the next vehicle(s) will arrive/depart in the given station from/to another station. It gets erased because the vehicles already departed, so there are no more estimative to do.
If a train stops at a signal, or a bus at a crossing, or a plane circles, then the departure board has to increase the time. The estimated times are msotly based on the distance travelled (and some further time for the last five tiles).
Where and how do I see these departure boards, if I'm not asking something far too daft here?
It's available in the latest nightlies. Will be available in next stable.