“Praying without ceasing” means at least three things.
First, it means that there is a spirit of dependence that should permeate all we do. This is the very spirit and essence of prayer. So, even when we are not speaking consciously to God, there is a deep, abiding dependence on him that is woven into the heart of faith. In that sense, we “pray” or have the spirit of prayer continuously.
Second – and I think this is what Paul has in mind most immediately – praying without ceasing means praying repeatedly and often. I base this on the use of the word “without ceasing” in Romans 1:9, where Paul says, “For God is my witness, who I serve with my spirit in the gospel of his Son, that without ceasing I mention you.” Now we can be sure that Paul did not mention the Romans every minute of his waking life, or even every minute of his prayers. He prayed about many other things. But he mentioned them over and over, and often. So “without ceasing” doesn’t mean that, verbally or mentally, we have to be speaking prayers every minute of the day in the fight for joy. It means we should pray over and over, and often. Our default mental state should be: “O God, help…”
Third, praying without ceasing means not giving up on prayer. Don’t ever come to a point in your life where you cease to pray at all. Don’t abandon the God of hope and say, “There’s no use praying.” Jesus is very jealous for us to learn this lesson. One of his parables is introduced by the words, “And he told them a parable to the effect tha tthey ought always to pray and not lose heart. He knew our experience in prayer would tempt us to quit altogether. So he, along with the apostle Paul, says, Never lose heart. Go on praying. Don’t cease.
– John Piper, When I Don’t Desire God: How to Fight For Joy, 157.