The terms 'Period Return' and 'Saver Return', used by others above, no longer exist. The Association of Train Operating Companies accepted that ticketing arrangements were too difficult to understand. There are now only 'Advance', 'Off Peak' (including 'Super Off Peak' on some routes, at certain times) and 'Anytime' tickets.
Eddie correctly states that 'Advance' tickets are only valid on the specified trains (and also, where reservations are included, only in the specified seats).
However where a ticket holder misses their train through a delay to an earlier service, an Advance ticket is automatically valid on the next train available. When a customer (with an Advance ticket) misses their train through other causes, station supervisors have discretionary authority to permit travel, without additional payment, on a later service.
In order to prevent abuse of the system, station supervisors are discouraged from permitting such travel other than exceptional circumstances but (having done the job myself) such authorisations do happen. In particular, when people have been travelling later than planned due to delayed flights, I've asked to see their flight boarding passes as evidence to show that they'd recently completed a flight.
Chris