> Consider when the algorithm places a point p and then samples its annulus to get a new point q.

I was confused for a while thinking p and q were swapped here, relative to the visualization below. [0] However I now think what I missed is that that the visualization is showing two points that are already firmly-established, and the question is where a potential third (unseen, unnamed) point could be placed.

So metaphorically speaking, it's about picking a new direction of travel that isn't guaranteed to be into your own recent footsteps.

[0] You might say I have problems minding my p's and q's.