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In Catholic theology, the doctrine of apostolic succession is that the apostolic tradition - including apostolic teaching, preaching, and authority - is handed down from the college of apostles to the college of bishops through the laying on of hands, as a permanent office in the Church. Historically, this has been understood as a succession in office, a succession of valid ordinations, or a succession of the entire college. It is understood as a sign and guarantee that the Church, both local and universal, is in diachronic continuity with the apostles; a necessary but insufficient guarantor thereof.
Papal primacy is different though related to apostolic succession as described here. The Catholic Church has traditionally claimed a unique leadership role for the Apostle Peter, believed to have been named by Jesus as head of the Apostles and as a focus of their unity, who became the first Bishop of Rome, and whose successors inherited the role and accordingly became the leaders of the worldwide Church as well. Even so, Catholicism acknowledges the papacy is built on apostolic succession, not the other way around. As such, apostolic succession is a foundational doctrine of authority in the Catholic Church.
Peter