One place St. Augustine discussed St. Paul's admonition to "pray without ceasing" is in a letter to Proba:
When we cherish uninterrupted desire along with the exercise of faith and hope and charity, we "pray always." But at certain stated hours and seasons we also use words in prayer to God, that by these signs of things we may admonish ourselves, and may acquaint ourselves with the measure of progress which we have made in this desire, and may more warmly excite ourselves to obtain an increase of its strength.... And therefore, what else is intended by the words of the apostle: "Pray without ceasing," than, "Desire without intermission, from Him who alone can give it, a happy life, which no life can be but that which is eternal"? This, therefore, let us desire continually from the Lord our God; and thus let us pray continually.
I think of prayer as a means of increasing in faith, hope, and charity. St. Augustine puts things the other way round, with prayer an expression of the theological virtues. As long as we possess faith, hope, and charity, we necessarily desire eternal life with God, and this desire, says St. Augustine, is prayer.
Which, when you look at it, matches perfectly with the traditional definition of prayer as "the raising of the heart and mind to God." If we have faith in God, our minds are raised to Him. If we love God, our hearts are raised to Him. If we hope in God, both minds and hearts are raised. (That's an overly systematic way of putting it, I suppose, but let it stand.)
St. Augustine goes on to suggest that specific acts of prayer are undertaken to support these virtues in three ways:
To admonish ourselves for our failings in faith, hope, and love.
To measure the progress we've made in faith, hope, and love.
To excite ourselves in the increase of faith, hope, and love.
This isn't all St. Augustine has to say about prayer, of course, but it's probably enough to meditate on for a few months.
[Laignappe: Remember St. Paul's "Rejoice always, pray always, give thanks always"? If you always have faith, hope, and charity, St. Augustine points out you are always praying. But you can no more always have faith, hope, and charity without always praying than you can without always rejoicing and always giving thanks.]