The offline edit is the main process of editing. When editing on film, they would use a "dupe" (a copy of the negative) with timecodes added to the negative to edit. This is the reason it is called "Off-line": It is using lesser quality copy to edit, as this will not produce damage on the negative. This is where the film is essentially created, with all the major decisions being made. They would mark out the timecodes, write them down, splice the film together and watch the sequences. The most common tools then were either the so called Moviola and later the Steenbeck table. The first part of an edit is often known as an "editor's cut", as it is an edit comprising all the scenes of the film, as written in the script. This often creates a film longer than what will be released. This is then screened with the director (who often joins in on the editing) and producers present, who discuss on how to move on. After this stage comes the fine trimming stage, where sequences are shortened, removed or re-edited to work better. Oftentimes some material is re-shot to better work with what now is a new version of the film (as a scene might be deleted, meaning info learnt from it is put into another scene). When it comes to music, the director and editor will edit to so called temp-tracks which is temporary music adding the rhythm and mood one would want in the sequence. After a new, more complete version is assembled, it is known as a workprint, which will then be screened again, now for more people and sometimes even the public. The state of workprints can differ greatly, with some being the finished film in all but name, to some having unfinished effects and temp-tracks. Eventually, the last decisions are made and the film is finished and then goes to the Online Edit for finishing.
On today's digital workflows, the work itself is not that different. The major difference now is now more technical, with the editing not compromising on working with timecodes, but instead editing files directly, allowing faster speed and simplicity. This form of editing is also called non-destructive as it doesn't alter the original files. In theory, this means that it could be made without the need for an Online Edit, but most films are still shot on film (then being scanned) and many digital formats are very processor heavy, instead leading to the use of proxy file which are files that are down converted to easier to edit format (the industry standard being Apple ProRes and Avid DNX).