It's all about eye shape
Once a group is surrounded, its fate depends entirely on the size and shape of the empty space it encloses — its 'eye space'. A space that can split into two separate eyes means life; a single connected space means death (the opponent fills it down to one eye, then captures). This chapter classifies the standard shapes by the number of empty points: how many you need to live unconditionally, and where the vital point is when you don't.