The following excerpt is from a podcast recorded by John Piper 4 years ago. Here is the link if you wish to listen to the 11 minute audio recording.
If you don't have time to listen, I've highlighted some important parts of his teaching:
John Piper:
“Pray without ceasing” (1 Thessalonians 5:17). If that life sounds hard to you — “pray without ceasing” — then Paul gives a specific example of the kind of prayer in 1 Thessalonians 5:18. It is not just, “Help, Lord,” which, of course, we would pray all the time. I need help to live this way. But he goes on and says, “Give thanks in all circumstances; for this is the will of God in Christ Jesus for you” (1 Thessalonians 5:18).
Let’s keep in mind two things about that context. One is the everys and the alls: “Do good always to everyone.” “Rejoice always.” “Pray always [or without ceasing].” “Give thanks always [or in every circumstance].” The other contextual observation is that there seems to be a deepening to the question “How? How to live?”
Answer: Do good always to everyone, even when they don’t do good to you. How? Rejoice always. Find your joy in something other than the way you are treated. How? Pray without ceasing. How? Be in a continual disposition of thankfulness to God.
Three Meanings
So, in those contexts, what does “pray without ceasing” mean? I see at least three things here that it means.
1. Spirit of Dependence
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: dependence. So, even when we are not speaking consciously to God, there is a deep, abiding dependence on him that is woven into the very essence of our faith.
In that sense, we are praying. We are experiencing a spirit of dependence continuously, and that kind of disposition is, I think, right at the heart of what God creates when he creates a Christian.
2. Repeated and Frequent
The second meaning that it has (and I think this is probably the one that is foremost in Paul’s conscious intention here) is that praying without ceasing means praying repeatedly and often. I base that on the way he used the word unceasing in Romans 1:9. Listen to how he uses the same word for without ceasing. He says, “For God is my witness, whom 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 make mention of the Romans in every minute or second of his prayers or his days or his preaching. He prayed and he spoke about lots of other things besides the Romans. But he mentioned them over and over. He mentioned them often. He mentioned them regularly. So he says, “I mentioned you without ceasing.”
It doesn’t mean that he was verbally and mentally always, every second, mentioning them. It means that over and over, always, repeatedly, without fail, when I get on my knees, you are in my prayer. That is basically what I think he means by “pray without ceasing” — repeatedly and often.
3. Staying Steadfast
The third thing I think he means is this: not giving up on prayer. “Without ceasing” means you should never come to a point in your life when you say, “Prayer doesn’t work. I am done. I am giving up on prayer.” That would be the very opposite of “without ceasing.” It means, “Don’t ever do that. Don’t ever get to that point.”
So, the key to rejoicing always is to pray continually — that is, to lean on God all the time and to call to him repeatedly and often. Never give up looking to him for help. Come to him repeatedly during the day, and come often. Make the default state of your mind a Godward longing and a Godward thankfulness.