"Running offline" is the process of starting a TP sequence out of time. Most, if not all sequencers, have some method of "audio mixdown" or "VSTi process" or similar methods. I didn't create such specific things because they are restrictive; instead, I created the "offline run" mode. The "Offline run" can "mixdown" anything, including midi.
What is offline run? Simply, you create the linking as you would wish to create. For example, for an audio mixdown, you would connect all your music output to an output file's ports. Then, starting the sequencer "offline" will complete that process much faster, as no time wait functions are applied.
A possible scenario is when yYou want to filter an existing audio track through a VST effect and to save it to another file track.
Normally now, you will want to press F5 to start recording. But since you don't want to listen, why wait? Simply press Shift+F5 (Or Offline Run from the menu) and the ASIO driver isn't started in reality, but a simulator starts that simply doesn't wait for the time to pass before running.
Note: Because ASIO is actually simulated, any linking rules that link to ASIO (or to midi in/out or wave in/out devices) are disabled when running offline.