Each station allows you to claim a single route. 

> A Train Station allows its owner to use **one, and only one, of the routes** belonging to another player, into (or out of) that city to help him connect the cities on his Destination Tickets.

(Emphasis mine.)

That route may be used to fulfill more more than one ticket.

> If a player uses the same Station to help connect cities on several different Tickets, he must use the same route into the city with the Station for all of those Tickets. The Train Station owner does not need to decide which route he will use until the end of the game.

For example, if you have a station at Berlin, you could claim the Berlin-Frankfurt route, and this may help you complete more than one destination ticket. You couldn't claim Berlin-Essen to complete a ticket that did not need Berlin-Frankfurt unless you also had a station on Essen.

[![Clip of the relevant portion of the board][1]][1]


  [1]: https://i.sstatic.net/bdkZe.jpg