絮 originally means 'cotton wadding / fluff' — fluff that piles up. As a verb it took on the meaning 'to repeat at length' (think how fluff just keeps coming). Pair with 嘴 ('mouth') and you get 'fluffy-mouthed' = chattering on and on.
register
Colloquial and slightly negative — implies the talker is wearing the listener out. 唠叨 (láodao) is a near-synonym used in the same kinds of family contexts.
