This refers to the lineage of ordination of a bishop. After Christ’s resurrection and ascension into heaven the apostles brought the faith throughout the known world and created communities of believers. Before leaving these new communities they would select people from among the faithful and lay hands on them in prayer imparting a permanent grace on their souls.
These bishops, as they would come to be known, would in turn do the same to future generations of bishops in an unbroken line of ordinations that continues to today.
Validly ordained bishops often maintain charts of their Apostolic Succession so they may trace their ordination back to one or more of the Apostles selected by Jesus Christ.
National Catholic Church of North America bishops are consecrated with what is known as the Duarte-Costa lineage; a valid, easily-traceable line of succession named after Roman Catholic Archbishop Carlos Duarte-Costa of Botucatu, Brazil, from whom the line originated in 1949.