Before jumping into this, its important to understand what exactly we mean by not only Apostolic, but also Mark.
First, a Mark is an inhierent trait observed in the Catholic Church. Specifically, four Marks are identified: One, Holy, Catholic, and Apostolic. What makes these Marks important is the fact that although other religions may possess a few of the traits, only the true Catholic Church can possess all four. Therefore, the Church and its importance derives from these marks, since they are what identify it as the true Church.
Now, we look specifically on the fourth mark: Apostolic. This term derives from the word Apostle, which as we know were the titles of Jesus' closest followers. Simply put, Apostolic means pertaining to the Apostles. The Apostles were entrusted by Christ to teach, sanctify, and govern the Church, which is the general reason why the Church is called Apostolic. However, the actual foundation for this claim can be observed in a set of what is like 3 sub-marks.
The Church was founded upon the Apostles in three different senses. The First pillar is Apostolic foundation, which states the Church is built upon the Apostles by Christ, The second is Apostolic Faith, which is the idea that the teachings of the Apostles are handed down and preserved through the Holy Spirit and the Church. Finally is Apostolic Succession, which states that the authority of the Apostles were handed down in the form of the college of bishops, and the Pope: successor of Peter.
In all of these ways, the Church has preserved the Authority of the Apostles, handed down thier teachings deriving from Christ, and we cannot forget that the entire goal of the Apostles was to establish help establish the Church, which implies we must treat the original Church they established--the Catholic Church--as the Church they originally intended to create. thererfore, the mark of Apostolic proves the Catholic Church is the true Church and most effective mean to achieve salvation.