[Jasper_]

Let's break it down:

Low res thin shell means that this is a model without many vertices. The "position based dynamics" is a more modern term for what was sometimes called "verlet integration", using the positions to compute immediately velocity relative to the ideal undeformed cage. So this is our simulation model. This is still how cloth sim is done today in games.

To compute the final render, Loop subdivision is used to turn the "thin shell" into a tighter model. You can Google for it, it's a way of subdividing triangles.

[logimame]

Position based dynamics is far more than just Verlet integration though. The meat of the algorithm has to do with dealing with various constraints (which is done by sequentially projecting positions related to each constraint while adhering to both the constraint and Newton’s laws (momentum conservation). PBD’s main strength is that it can incorporate various types of constraints at once with relatively simple code and good performance.