There are few more succinct, helpful descriptions of prayer than this one from John Calvin's Institutes of the Christian Religion (Book 3, Chapter 20, Sect. 2):
To prayer, then, are we indebted for penetrating to those riches that are treasured up for us with our heavenly Father. For there is a kind of intercourse between God and men by which, having entered the upper sanctuary, they appear before Him and appeal to His promises, that when necessity requires they may learn by experiences that what they believed, merely on the authority of His Word, was not in vain. Accordingly, we see that nothing is set before us as an object of expectation from the Lord that we are not enjoined to ask of Him in prayer, so true it is that prayer digs up those treasures that the Gospel of our Lord discovers to the eye of faith.
The necessity and utility of this exercise of prayer no words can sufficiently express. Assuredly, it is not without cause our heavenly Father declares that our only safety is in calling upon His name (Joel 2:32). By it, we invoke the presence of His providence to watch over our interests; of His power to sustain us when weak and almost fainting; of His goodness to receive us into favor, though miserably loaded with sin; in fine, [we] call upon Him to manifest Himself to us in all His perfections. Hence, admirable peace and tranquility are given to our consciences; for the [necessities] by which we were pressed being laid before the Lord, we rest fully satisfied with the assurance that none of our evils are unknown to Him, and that He is both able and willing to make the best provision for us.