The Ascension is the event, where Jesus arose into heaven, at the end of his time on earth.
Jesus' time on earth began with his birth. It was interrupted for three days by His death on the Cross. During that time, He descended into the realm of the dead and preached the Gospel to the good people who died before Him. This allowed those good and holy souls--the righteous dead, as we call them--who accepted Christ as their Savior to proceed to heaven. On the third day after his death and burial, Jesus Christ was raised from the dead, an event we call the Resurrection. He spent the next 40 days preaching and preparing His disciples to perform the work of preaching and baptizing all people.
At the end of this 40 day period, Jesus ascended into heaven. We call this the Ascension.
The Bible tells us what happened on that day:
In my earlier work, Theophilus, I dealt with everything Jesus had done and taught from the beginning until the day he gave his instructions to the apostles he had chosen through the Holy Spirit, and was taken up to heaven.
"He had shown himself alive to them after his Passion by many demonstrations: for forty days he had continued to appear to them and tell them about the kingdom of God.
While at table with them, he had told them not to leave Jerusalem, but to wait there for what the Father had promised. 'It is', he had said, 'what you have heard me speak about: John baptised with water but, not many days from now, you are going to be baptised with the Holy Spirit.' Now having met together, they asked him, 'Lord, has the time come for you to restore the kingdom to Israel?' He replied, 'It is not for you to know times or dates that the Father has decided by his own authority, but you will receive the power of the Holy Spirit which will come on you, and then you will be my witnesses not only in Jerusalem but throughout Judaea and Samaria, and indeed to earth's remotest end.' As he said this he was lifted up while they looked on, and a cloud took him from their sight. They were still staring into the sky as he went, when suddenly two men in white were standing beside them, and they said, 'Why are you Galileans standing here looking into the sky? This Jesus who has been taken up from you into heaven will come back in the same way as you have seen him go to heaven.' " Acts 1:1-11
It is said that by His death and Resurrection, Jesus opened the gates of heaven for all humanity. This is true, and His Ascension demonstrates this to us. It is His proof that those of us who believe in Him in faith and follow Him will also be raised on the last day, and enter into heaven.
From heaven, Jesus hears our prayers and intercedes for us with His Father.
We celebrate this on Ascension Sunday, which is celebrated forty days after Easter. Traditionally it is celebrated on a Thursday as a Holy Day of Obligation. The Church presently observes it on a Sunday to allow more of the faithful to attend Mass. It remains a Holy Day of Obligation, and the faithful are reminded that all Sundays are obligatory by default.
The Ascension should not be confused with Pentecost, which is celebrated 50 days after Easter. Pentecost commemorates the descent of the Holy Spirit on the disciples of Christ, after His Ascension.