"The express image" is from a single Greek word, from which comes our word "character." The word appears only here in the New Testament.
William Barclay explains that it literally describes "the impress that a seal leaves on wax," so he renders that part of Hebrews 1:3 as, "He [Christ] is the exact impression of his [Father's] being, just as the mark is the exact impression of the seal." Physically, a seal can make an impression only by making contact, which is exactly what must happen to us spiritually. For God to make us in His "express image"—to stamp His character on us, to give us the gift of His qualities—requires contact, that we be in His presence. Praying always does just that.
This verse also suggests that godly character is not really the result of battling temptation, a battle we are powerless to win on our own. Rather, character is created by our continual, conscious choice to be in contact with Him, to submit everything we are to Him, to acknowledge that He is the only source of strength, and then to trust—to have faith in (I John 5:4)—His love and willingness to do battle for us, to give us the gift of His character.
Praying always is that first step in overcoming—submitting. Then He can take over to do what we are not able to do on our own. After our decision to submit, He may still require certain actions from us, to take those few steps in faith—our walk with God—but then we have Him on our side, giving us guidance and strength.
Even in the world, we can see the power of character. While character can make an ordinary man extraordinary, a lack of character can make an extraordinary man quite ordinary. Character has power because it connects us with divine wisdom. Without character, we are limited to human intelligence, and most of history is a record of its woeful inadequacy. Character links us to a godly intelligence that can see the end from the beginning (Isaiah 46:10). A person who exercises character exercises faith. He may not foresee the good it will bring, but he trusts that the divine intelligence behind his faith knows more.
If we are not continually praying, we will be using human intelligence with the same ratio of success that history has shown it to have. Praying always, striving always to be aware of His presence, allows His Spirit to rub off on us. God has chosen praying always as a primary method to allow us to get to know Him, to receive His character as a gift, to overcome, and to receive eternal life and salvation.
If God has given us this powerful tool, why do we not use it more? Why do we not seek God for every decision, every thought?