Use this when an emotional or moral pressure makes some action unavoidable — you literally cannot leave it undone. It is stronger and more subjective than ～なければならない (obligation) and more emphatic than つい～てしまう; the speaker is describing an impulse they could not suppress. In writing and formal speech the near-synonym ～ずにはいられない is more common, while ～ないではいられない sounds slightly more conversational and emotive.