A No Objection Certificate request asks your employer to state formally that they have no objection to something you are doing outside your job — travelling, studying part-time, taking a second role, or applying for a visa. Say exactly what the NOC is for and who will receive it, because the wording an embassy needs is different from what a university needs.
A short letter from your employer stating they have no objection to something you are doing — travel, study, a second job, a loan application. It is not a legal permission; it is documented awareness and consent.
HR, on company letterhead, with an authorised signature and usually a company stamp. Your line manager's email approval is not normally accepted by embassies or banks.
Typically three to ten working days. Ask early, especially for visa appointments, and give HR the exact addressee and wording the receiving body requires.