From BiblePortal Wikipedia

Webster's Dictionary [1]

(1): (a.) Pertaining to an apostle, or to the apostles, their times, or their peculiar spirit; as, an apostolical mission; the apostolic age.

(2): (a.) According to the doctrines of the apostles; delivered or taught by the apostles; as, apostolic faith or practice.

(3): (a.) Of or pertaining to the pope or the papacy; papal.

Charles Buck Theological Dictionary [2]

Apostolical; something that relates to the apostles, or descends from them. Thus we say the apostolican age, apostolical doctrine, apostolical character, constitution, traditions, &c

Cyclopedia of Biblical, Theological and Ecclesiastical Literature [3]

See (1), an episcopal seat founded by an apostle; (2) a title given to the three sees of Antioch, Ephesus, and Rome.