Day and Night Worship and Prayer : The Means or the End?

Both.

"Night and day prayer is both part of the means and part of the end of the Kingdom of God coming to the earth. That is - through history, whenever night and day prayer has taken place over a sustained period in a particular location a move of God has not been far behind. And, when God does move in answer to prayer, part of the result is more worship and prayer. Part of our destiny is night and day prayer and worship around the throne of God, and part of how we will get there is the church continually crying out day and night for justice!" (via SHOP)

Or as John Piper says in his book Let The Nations Be Glad:

"Worship, therefore, is the fuel and goal of missions. It’s the goal of missions because in missions we simply aim to bring the nations into the white hot enjoyment of God’s glory."