The Kingdom of God
The return of Jesus is implied by the use of the term 'Christ' in Peter’s speech; it is also referred to in a second indirect way.
"For David did not ascend into the heavens, but he himself says, ‘The Lord said to my Lord, “Sit at my right hand, until I make your enemies your footstool.” (Acts 2:34,35)
This makes three points:
First, it shows that the passage in question doesn’t refer to David but to David’s descendant: David didn’t ascend to the heavens, but this descendant has done exactly that.
Second, it tells us that Jesus sits at the right hand of God, the position of honour in the ancient world.
Finally, Jesus remains in heaven until the time at which God defeats his enemies. This means that there is to be a time when Jesus returns.
Jesus is to return on the day of judgement, to be the judge of the world. At this point the world will be transformed to the state that God intended it to have, and it will remain like this for ever. This time after judgement is called the 'Kingdom of God'. It is described in many passages in the Old Testament - for example Isaiah 65:17-25.
These passages tell us that the Kingdom of God is to be a time of peace, of prosperity and of happiness. In the end suffering will cease and there will be eternal life in union with God. This kingdom is the hope of the Gospel. These are the conditions that are to exist after the return of Jesus and the day of judgement.
The Kingdom of God is the hope for mankind.