Offline editing, was almost standard when non-linear video editing started, because of hard disk memory mostly. It was easier to digitise your rushes at a low video resolution, especially in longer form high shooting ratio programmes and films. As the previous person says, at the end of the edit, a 'conforming' session took place, whereby the sequence was rebuilt, at full resolution (but only the actual shots in the final cut)
With sound it was a slightly differing story. During offline digitising, the audio was usually taken in at 48khz digital, so it was technically ok for broadcast. So in theory the final cut audio tracks could simply exported to the sound mix. Sometimes however, for various reasons, the audio was also conformed, using an EDL ( for example a CMX3600 C mode list) The sound editor would load up each audio rushes tape and import Just the audio referenced by the edit ( with suitable handles for mixing/ramping)
To dig deeper, sometimes the audio digitised with the rushes was a mix of various microphones, taken from a digi beta tape or SX or Beta SP. The original sound rushes having been recorded onto DAT tape for example. In this scenario it was of course necessary to redigitise (I.e. Conform) the audio at the end of the edit, to make sure all the original sound tracks were imported into the sound editors system. They effectively then used the editors final soundtrack as a guide to check sync etc, but they would rebuild the soundtrack using the digital rushes.
There was another distinction about offline/online editing, whereby a traditional 'film editor' would be called an offline editor and a traditional VT editor would becalmed an online editor. The implication being that offline editors were more used to editing from scratch, without the director present for assembly work.
(Film of course was the original non-linear medium, as usually the editor cut a positive print copy of the originally shot negative)
Nowadays, by and large an ON line editor is someone who is very accomplished at compositing, effects work, quick turnaround high-end work, and an offline editor restricts themselves to cutting the film or programme. however these boundaries are breaking down fast now, with many editors able and forced to do everything from start to finish - and crucially now it is possible to edit full resolution video in the initial non-linear edit, removing the need for a conforming session.