。
She suddenly butted into our conversation.
Literal
She [topic-は] suddenly we [possessive-の] conversation [into-に] mouth [object-を] inserted.
口を挟む is a body-part idiom — 'to insert one's mouth' — for butting into a conversation. The 挟む verb literally means 'to pinch / wedge between,' so the image is one of forcing your mouth into a gap in the talk. There's a near-synonym 口を出す ('to put your mouth out' = to meddle, butt in), with the difference being subtle: 口を挟む emphasizes the interruption itself, while 口を出す often emphasizes meddling with someone else's affairs. Both are everyday idioms; both carry mild disapproval.