Champaran HumSafar Express : इन अजनबी सी राहों में, जो तू मेरा हमसफ़र हो जाये, बीत जाए पल भर में ये वक़्त, और हसीन सफ़र हो जाये. - Piyush Singh

How is a PNR number generated for a train in the Indian railway?
Passenger name record (PNR) number is a unique pointer to a record in the railway database. The record pointed by PNR contains comprehensive journey details.
The answer by Anonymous is thus completely misleading. The PNR number itself doesn't store any data about the individual. Instead, it points to a unique record in the central database, which actually holds all the information of the journey. Let's see how it's generated.
First...
more...

3 Digits:-
They tell us from which PRS the ticket has been booked.
The PNR Numbers' starting digit does not depend on the PRS from which it has been booked.
It actually depends upon: Zone of the Train, w.r.t. starting station of the train.
2,3: NR, NCR, NWR, NER
4,5: SR, SWR, SCR
6,7: NFR, ECR, ER, ECoR, SER, SECR
8,9: CR, WCR, WR
e.g. If a ticket is booked in Rajdhani Express (Mumbai to New Delhi), as the starting station is Mumbai, PNR will start from 8.
The subsequent 2 digits detail specific PRS.
Last 7 Digits :
They are randomly generated numbers. They represent no information.
PNR number lasts minimum 9 month as the TDR filed can take maximum of 9 months. It then flushed out. (Normally)
After a year, the same PNR number can be generated.