While playing Metal Gear Solid V and having a Base Dev Team, occasionally you'll get a little popup box in the bottom right of the screen mentioning how much of each resource type was extracted or refined, resulting in a bit of passive resource gain over time. More rarely, you'll see a "Online Materials Automated Mining" or "Online Materials Processing" popup, with much larger quantities of materials. Given the distinction between online and offline in the rest of the game, I'd guess that this kind of resource gain can still happen while not playing the game, but I couldn't find anything confirming or denying it. So what is the diffeerence?
Offline materials come from three sources:
Materials you pick up in the field. Processed materials in small crates go directly to your material totals every checkpoint. Unprocessed materials in containers go into an offline queue.
Periodic conversion of materials in the offline queue. Every time this conversion ticks, 10% of your unprocessed materials are converted to processed materials.
Periodic mining done on Mother Base itself.
Online materials come from two sources:
Periodic conversion of unprocessed online materials. The conversion rate here is 30%. You get unprocessed online materials by extracting crates or as rewards in FOB missions.
Periodic mining done on your FOBs. The amount of each material you gain at each of these ticks depends on the quantity of material deposits where your FOB is located (which you can see when you purchase the FOB or in the FOB information screen).
The offline sources can only tick while you are actively playing the game. The online sources tick in "real time," more or less, so you can stop playing for a while and come back to find yourself quite rich.
I got most of this information from this person's rather extensive post on GameFAQs. It includes quite a bit more information, including detailed descriptions of each processing interval.