And when he had said these things, as they were looking on, he was lifted up, and a cloud took him out of their sight. And while they were gazing into heaven as he went, behold, two men stood by them in white robes, and said, “Men of Galilee, why do you stand looking into heaven? This Jesus, who was taken up from you into heaven, will come in the same way as you saw him go into heaven.” - Acts 1:9-11
In the minds of the apostles the ascension of Jesus was as important as his life, death, and resurrection. It was the same for the early church fathers. Both the Apostles' and Nicene Creeds confess that Jesus ascended into Heaven, to a place of honor at the right hand of the Father, from which he will return to judge the living and the dead. A contemporary expression is found in the popular praise chorus: "From the cross to the grave/From the grave to the sky/Lord, I lift Your name on high."
Though the disciples couldn't comprehend it at the time, it was better for them that Jesus returned to the Father. "Do not cling to me," the risen Jesus says to Mary Magdalene (John 20:17). The ascension unleashed a multitude of benefits, not least of which was the sending of the Holy Spirit. The ascension was the crowning achievement of Christ's work. It was like a detonator that unleashed the power of Christmas, Good Friday and Easter beyond the bounds of time and space.
In being taken up Jesus was once again taking on all the attributes of glory he enjoyed since before the world began. It marked the end of the temporary "emptying" that the Apostle Paul writes about in Philippians 2. But there's more. In a real sense the ascension was a taking up into glory of human nature in an entirely new way. Jesus didn't cast off his human nature when he returned to the Father. This is why the New Testament writers can make such astonishing claims about the believer's present union with Christ. Paul goes so far as to say that we are seated with Christ in the heavenly places (Eph. 2:6, see also Col. 3:3-4). I think he means that more literally than we are apt to take it.
The Reformation Study Bible (Ligonier, 2005) summarizes three facts established by The Ascension.
Christ's personal ascendancy. Ascension means accession. To sit at the Father's right hand is to occupy the position of ruler on God's behalf (Matt. 28:18; 1 Cor. 15:27; Eph. 1:20-22; 1 Peter 3:22).
Christ's spiritual omnipresence. In the heavenly sanctuary of the heavenly Zion (Heb. 9:24; 12:22-24), Jesus is accessible to all who invoke His name (Heb. 4:14), and powerful to help them, anywhere in the world (Heb. 4:16; 7:25; 13:6-8).
Christ's heavenly ministry. The reigning Lord intercedes for His people (Rom. 8:34; Heb. 7:25). Though requesting from the Father is part of what He does (John 14:16), the essence of Christ's intercession is intervention in our interest rather than supplication on our behalf (as if His position were one of sympathy without status or authority). In sovereignty He now lavishes upon us the benefits that His suffering won for us. From his throne He sends the Holy Spirit constantly to enrich His people (John 16:7-14: Acts 2:33) and equip them for service (Eph. 4:8-12).
Further Reading: Was Jesus the first spaceman?