Does an instant played in response to a sorcery actually resolve before the sorcery?

When a player casts a sorcery, it goes on the stack and players receive priority to respond (CR 116.3). If an opponent then casts an instant, that instant is placed on top of the stack above the sorcery. The stack always resolves from the top down — last in, first out — so the instant resolves before the sorcery does (CR 608.1).

This is the fundamental purpose of the stack: it lets spells and abilities 'queue up' in a defined order. Nothing on the stack resolves until all players pass priority in succession without adding anything new (CR 116.4). Once that happens, only the top object resolves, and then players get priority again before the next object resolves.

It's worth noting that you normally cannot cast a sorcery in response to anything (CR 307.1) — sorceries can only be cast during your main phase when the stack is empty. But an opponent can respond to your sorcery with an instant, and that instant will always resolve first.

Concrete example: You cast Divination (a sorcery). Before it resolves, your opponent casts Counterspell targeting it. Counterspell is now on top of the stack. After both players pass priority, Counterspell resolves first — countering Divination. Divination never resolves.

This interaction is governed by CR 405.6 (stack resolves top to bottom), CR 608.1 (resolving spells), and CR 116.3–116.4 (priority and passing).