My mother snapped her handbag shut.

Literal

Mother [topic-は] snap [quotative-と] handbag [object-を] closed

ぱちっと = a mimetic for a crisp snapping or clicking sound. と marks it as an adverbial manner. ハンドバッグを閉めた = 'closed the handbag.' The mimetic makes the action vivid and audible.