noun
Definition 1
Aptitude for any special kind of action.
Source: Concise Oxford Dictionary
Context: They [Asia's leading tycoons] have the ear of presidents, a preternatural ability to win government favours and an unnerving faculty for floating above the concerns of ordinary businessmen.
Source: Financial Times 30/07/2007 (editorial)
Definition 2
Liberty of doing something given by law or a superior; authorisation, licence.
Source: Concise Oxford Dictionary
Context: It creates a Register of General Terms. The inscription of terms in it is not obligatory, but the Government has the faculty of obliging certain economic sectors to register their general terms.
Source: ec.europa.eu/consumers
Definition 3
Teaching department of a university.
Source: Invertext, from Concise Oxford University
Context: [In India] even engineering faculties struggle to find academic staff.
Source: Financial Times 15/10/2009