嗅 is more formal/written than 闻 (wén), which is the everyday word for 'to smell.' 嗅觉 (xiùjué, sense of smell) is the standard term. 嗅 often implies deliberate sniffing, while 闻 can mean simply noticing a smell.
Left mouth radical — the indexing radical, marking 嗅 as an action of the face/respiratory system. Pictograph of an open mouth, square-shaped. Anchors the entry in the broad mouth-action family with 吃 eat, 喝 drink, 吹 blow, 吸 inhale.
Right 臭 (self + dog) supplies both sound (xiù, exact match) and meaning: a dog using its nose to detect scent. The original 臭 read xiù 'to smell' before later shifting to chòu 'stink'; 嗅 was created with an added mouth radical to preserve the verbal sense of 'sniffing'.