Abbreviation of 'operation' or 'operation/surgery.' In medical contexts it often means 'surgery'; more generally used colloquially for an operation or task.
明日、親友がオペを受けるので病院に付き添う。
My close friend is having surgery tomorrow, so I'll accompany them to the hospital.
システムのオペを夜間に行う予定です（＝オペレーションを行う）。
We plan to perform the system operation at night (i.e., carry out the operation).
救急センターではチームが連携してオペを成功させた。
At the emergency center, the team worked together to successfully carry out the operation (surgery).