It means that either the train is not going to start its journey from the source station or it will not reach its destination station. In simple terms, a train that won't complete its full journey is called a partially cancelled train. This happens only in emergency situations like technical faults, accidents, natural disasters, thunderstorms, strikes, and many more.
Let’s say a train starts its journey from Lokmanya Tilak Terminus to Lucknow Junction, but some technical issue or natural calamities occurs during its running, and due to that, the train is running late for more than acceptable time, and somehow it's not possible to cancel the train. In that case, it will be given a halt at Orai or Kanpur Ctrl or any nearby major station, and it will not be allowed to reach the destination. That's why it's partially cancelled to maintain time.
If the Indian railway fails to make alternate arrangements or the passenger is not willing to make use of alternate arrangements provided by the railway, in both cases, the full fare for the untraveled portion after retaining the fare for the traveled portion will be refunded to the passenger.