You probably used to use a VCR, with VHS tapes. All VCRs had a TV tuner built into them, so you didn't need to use another tuner to receive the signal. You could also watch one programme while recording another because the VCR's tuner fed a signal to the tape, while the TV's tuner fed a different signal to the screen.
However, many (possibly most?) DVD recorders don't have a TV tuner built in. They rely on using an external tuner (either from a TV or from a Freeview box). If you've got such a recorder, you can only record the signal from the TV's tuner, which means that the TV must be turned on.
To get back to a situation similar to the one you used to have with your old VCR, you need to add another tuner to the system. This either means replacing your DVD recorder with one that includes its own tuner or (far cheaper) purchasing a Freeview box to provide your existing DVD recorder with a tuner that it can take a signal from. You'd then be able to watch one programme while recording another. However, you'd have to remember to leave the Freeview box (instead of the TV) turned on when making recordings.
Chris