It's a deep topic and one that will not allow us to completely plumb its depths. Essentially, it's communication with our relational God. But because we are dealing with God, we will find ourselves treading water, but never ever touching bottom.
Yet, how is it we have this need to quantify and boxify this amazing gift?! Humans have tried desperately to know God and understand Him in any way they can. We will never ever understand how God works through prayer... if it's because we pray that He works and answers... or because He is God and will not be trifled with... or because prayer ultimately proves that we are nothing and He is everything and that through Him all things exist and He exists to prove His glory... or a combination of all of the above. It really does not matter.
What matters, though, is God and who He is. When we know who He is, we can rest assured that whatever we pray will be answered in His perfect time because He is good and everything He does is for our good - His glory.
Quantifying an A+B=C formula will not give us peace of mind in understanding the ways in which God works. It will not build trust in His ways. We'll begin to create chess-like moves so He will respond in predictable ways. We forget Isaiah 55:8-9... (btw, this passage is an amazing box-buster!)
8 “For my thoughts are not your thoughts,
neither are your ways my ways,”
declares the LORD.
9 “As the heavens are higher than the earth,
so are my ways higher than your ways
and my thoughts than your thoughts.
He works independently and with no need of us,
yet wants us to know He cares about what worries us.
He is completely other than us,
yet His son obediently put on flesh and bone.
He exists before the beginning of time,
yet He chose to be born and to die within the constraints of time.
We live inside this box called time. We want to control what happens to us. We embrace the fact that God loves us and leap to the incorrect conclusion that He must want to do what we ask of Him.
We are only able to believe that God loves us because our innate sinfulness has been covered by His Son's righteousness. He could never even look at us without destroying us for our sin. We come as beggars; as nothing without Him. This tiny fact is often obscured in the most well-meaning gospel messages.
We must cling to the fact that we are nothing without Him so that we can leap to the glorious conclusion that He loves us and will bring everything into our lives for one purpose to show His glory through us.
That is reason enough to pray.