I was watching a TV preacher the other day tell his viewers, "There's power in prayer so pray!" He seemed to be saying that the one who prays has the power to make things happened.
I like Michael W. Newman's viewpoint much better: Jesus also bid His disciples to pray. The power of prayer is not as much in your speaking as it is in God's listening. Implicit in prayer is the promise that God hears you and responds. When you are overcome by anxiety, you can cast your cares upon your Lord and Savior, being confident that He will carry the burden and lighten the load.
From, "Hope When Your Heart Breaks," page 192