This feature covers the option of transferring a recording from HDD to DVD and - during the copy - lower the quality in order for the programme to fit the disc.

For example if you have recorded a programme on the HDD at the highest quality for 2 hours, then you don't have enough room on a single-layer DVD to store the programme in full quality. You'll have to sacrifice quality for size.

Can the recorder then (in RealTime) "play back" the programme from the HDD while simultaneously "record" the programme onto DVD at a lower quality in order for it to fit the disc?

On some recorders, this option is called "Rec Mode Coversion Dubbing", on others it's simply called "RealTime Copy" or "Optimized Copy".