If a cargo is not demanded at the current station but is demanded at a later station, it stays on the train, otherwise it is delivered at the current station. Store Undemanded cargoes are stored at the current station, and can be picked up by any train. Note, even the train that dropped them off can pick them up, so be sure to change your train's consist at this station or else you'll immediately pick up what you've just dropped off. Deliver Undemanded cargoes are delivered at the current station. You won't receive much money, though.
Undemanded cargoes stay on the train, presumably for delivery or storage at a later station.
Note, if you have this option set at all your stops, an undemanded cargo will stay on your train indefinitely. Most of the time, when routing a train, you just want to pick the stations and let the computer find the best route. However, there are situations where your track grid can grow complex and you want to override the automatic route finding and specify exactly how a train should go. Your train will travel to that point before traveling on to its next station. Two new choices have been added to the Game Options window, under the gameplay section.