Why pressure and not just springs
A mass-spring shell is the standard way to build a deformable object, and on its own it does not work for jelly. Without something holding the interior out, the shell collapses inward under its own constraints and reads as a deflated balloon rather than as a solid soft body.
The pressure term fixes that by treating the mesh as enclosing a volume. Every vertex is pushed along its area-weighted normal in proportion to how far the current enclosed volume has drifted from the rest volume, so a squeezed jelly pushes back everywhere at once rather than only where the springs are stretched.
That is also where the jiggle comes from. Pressure and springs restore the shape on slightly different timescales, so a compressed jelly overshoots on the way back and oscillates, which is exactly what real jelly does and exactly what makes the footage watchable.

