This is perhaps a rather over-used catch-phrase within the Christian Community. I've certainly heard it often enough.
However, where ever it's origins, it's taken on more of a mantra effect...something's gone wrong, I can't get control of my life, and the obvious advice is...
But that's wrong. You can't give control to God if you don't have a relationship with Him.
The whole idea of having a close personal relationship with God, while having been submerged for a number of centuries by the Holy Roman Catholic Church, (who wanted all of the salvific stuff to go through them, rather than direct line) has found an re-emergence in recent centuries. (My thanks to those who pointed this out in detail.)
If God is just this nebulous being of power whom you worship, then control is more of a matter of fate, and you probably make most of your daily decisions on an immediate basis.
On the other hand...If you truly are in a state of Faith Seeking Understanding, then God is someone you're trying to grow closer to, and to whom you can truly begin to turn control over to.
Just as forgiveness, truly, is admitting that God can handle justice much better than yourself, "letting God" is a state of seeking God's guidance and support in life, rather than just depending on your own understanding. But unless that state of seeking and willingness is there... it's just an empty phrase.