The Catechism of the Council of Trent explains why Christ ascended into Heaven:
First of all, He ascended because the glorious kingdom of the highest heavens, not the obscure abode of this earth, presented a suitable dwelling place for Him whose body, rising from the tomb, was clothed with the glory of immortality.
He ascended, however, not only to possess the throne of glory and the kingdom which He had merited by His blood, but also to attend to whatever regards our salvation.
Again, He ascended to prove thereby that His kingdom is not of this world. For the kingdoms of this world are earthly and transient, and are based upon wealth and the power of the flesh; but the kingdom of Christ is not, as the Jews expected, earthly, but spiritual and eternal. Its resources and riches, too, are spiritual, as He showed by placing His throne in the heavens, where they are counted richer and wealthier who seek most earnestly the things that are of God, according to these words of St. James: Hath not God chosen the poor in this world, rich in faith, and heirs of the kingdom which God hath promised to them that love him?
He also ascended into heaven in order to teach us to follow Him thither in mind and heart. For as by His death and Resurrection He bequeathed to us an example of dying and rising again in spirit, so by His Ascension He teaches and instructs us that though dwelling on earth, we should raise ourselves in desire to heaven, confessing that we are pilgrims and strangers on the earth, seeking a country and that we are fellow-citizens with the saints, and the domestics of God, for, says the same Apostle, our conversation is in heaven.