Black can only get one eye out of the 2x2 space, unless Black can make two diagonal moves in there. After , Black must connect to live and also make an eye at a.
If Black tries to capture first with , White attacks the eye at . Black cannot solidify the eye at a because of shortage of liberties, and if Black captures the two white stones, the eye becomes false when White plays at a.
This does not work. is forced, to prevent Black getting two eyes directly by capturing at ; and solidifies the eye at a. White needs three moves to capture any black stones while Black needs only one to capture the inside white stones (and remove the aji - lingering aftereffects -, so White doesn't even have a ko threat here).
If is played at , Black must sacrifice the three stones in the upper right and form two eyes at