From the New Advent web site
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(Greek euchesthai, Latin precari, French prier, to plead, to beg, to ask earnestly).
An act of the virtue of religion which consists in asking proper gifts or graces from God. In a more general sense it is the application of the mind to Divine things, not merely to acquire a knowledge of them but to make use of such knowledge as a means of union with God. This may be done by acts of praise and thanksgiving, but petition is the principal act of prayer.
The words used to express it in Scripture are: to call up (Genesis 4:26); to intercede (Job 22:10); to mediate (Isaiah 53:10); to consult (1 Samuel 28:6); to beseech (Exodus 32:11); and, very commonly, to cry out to. The Fathers speak of it as the elevation of the mind to God with a view to asking proper things from Him (St. John Damascene, On the Orthodox Faith III.24); communing and conversing with God (St. Gregory of Nyssa, "De oratione dom.", in P.G., XLIV, 1125); talking with God (St. John Chrysostom, "Hom. xxx in Gen.", n. 5, in P.G., LIII, 280). It is therefore the expression of our desires to God whether for ourselves or others. This expression is not intended to instruct or direct God what to do, but to appeal to His goodness for the things we need; and the appeal is necessary, not because He is ignorant of our needs or sentiments, but to give definite form to our desires, to concentrate our whole attention on what we have to recommend to Him, to help us appreciate our close personal relation with Him. The expression need not be external or vocal; internal or mental is sufficient.
By prayer we acknowledge God's power and goodness, our own neediness and dependence. It is therefore an act of the virtue of religion implying the deepest reverence for God and habituating us to look to Him for everything, not merely because the thing asked be good in itself, or advantageous to us, but chiefly because we wish it as a gift of God, and not otherwise, no matter how good or desirable it may seem to us. Prayer presupposes faith in God and hope in His goodness. By both, God, to whom we pray, moves us to prayer. Our knowledge of God by the light of natural reason also inspires us to look to Him for help, but such prayer lacks supernatural inspiration, and though it may avail to keep us from losing our natural knowledge of God and trust in Him, or, to some extent, from offending Him, it cannot positively dispose us to receive His graces.
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