I don’t get what stability is when it comes to yoyos and how it effects play. Can someone please tell me?

Stability deals with how ‘straight’ the yoyo will remain when doing tricks. Think of a bicycle wheel or a fly wheel. With the weight concentrated on the outside, it helps keep it in a fixed position. Yoyos with little rim weight will die out on you and tilt easily, forcing you to be more careful with your moves. The Popstar is good for not being ultra stable but at the same time, forces you to have pinpoint accuracy if you want to keep a long combo going.

Other yoyos that are more stable (and have more rim weight/thicker rims compared to the body) would probably be the Dark Magic, FH2010, any throw with weight rings, or something like the Superstar or RecRev No. 9 (which I find ultra stable).

Some yoyos can have stability improved with weight rings, something I did to my Lyn Fury. Plays a bit more stable now.