I am currently at work on a manuscript that encompasses this very topic. I would like to share here some of my thoughts along these lines:
I believe that this concept that originates in Yahweh (the God of Israel and of the followers of Christ) and that all other versions are responses to this innate truth that God has built into us as His creation. I also believe that this concept is central in Scripture. There is one Hebrew word for it and one Greek word; but translators have used many to convey it to us in English...Purity, pure of heart, single, unity, united, integrity, single-mindedness, etc...and this has diluted the impact of the concept for us.
Mindfulness plays a big part in being single of heart and purpose...We need to know for what we are aiming and whether or not we deviate from that path on a moment by moment basis. It also involves a comprehension or knowledge of ourselves: what we were created for in general and also in specific. How many of us KNOW why God placed us, in our particular set of circumstances and personality, on this earth...and what does He want us to do with that understanding?
Singleness of heart must also play a part in our prayer life. (How often do we pray mindlessly-- "God bless so and so" or "please heal so and so" but then not really expect that He will?) Our requests to God must match the level of faith that we have and our whole being needs to be engaged and united in the focus of our prayer. Look at this passage from James chapter one:
If any of you lacks wisdom, he should ask God, who gives generously to all without finding fault, and it will be given to him. But when he asks, he must believe and not doubt, because he who doubts is like a wave of the sea, blown and tossed by the wind. That man should not think he will receive anything from the Lord; he is a double-minded man, unstable in all he does. (James 1:5-8 NIV )
Although speaking of double-mindedness, it is also a comment on God's view of single- mindedness. Plus there is Jesus' statement in the list of those people who are blessed or happy: "Blessed are the pure in heart, for they shall see God." Have you ever really meditated on what it means to be pure of heart? ...or asked God to reveal it to you in your circumstances to show you what that virtue should look like in your own life? To do this is the first step in a mindful life.
We need to have our entire beings: mind, soul, strength (our actions and our physical beings), and heart , all focused on the pursuit of that which God has entrusted to us to accomplish with our lives; to be in His presence; and to arrive at someday when we enter His kingdom. (By the way, you may recognize here that we are to LOVE God with our entirety; that is all of our main goal...but how do we each do that by obeying His calling to us? That is my question to you.) This DOING has much to do with BEING and also with BECOMING. It is all one. And we need to be "one" as well. That's the whole point.