For a theurgist, prayer is one of the main tools of the trade. Here is an extract from a prayer book that describes the basics of prayer's function. In later posts I'll cover the origins of why Jews pray three times per day and the four levels of ascent in prayer.
A new translation and anthologised commentary by Rabbi Nosson Scherman
Published by Mesorah Publications, Ltd, Second edition (first impression February 1987)
Its Hebrew name is tefillah, a word that gives us an insight into the Torah's concept of prayer. The root of tefillah is [the letters] Peh-Lamed-Lamed, to judge, to differentiate, to clarify, to decide. In life, we constantly sort out evidence from rumour, valid options from wild speculations, fact from fancy.
The exercise of such judgement is called Puhliah. Indeed the word Pehlilim (from Peh-Lamed-Lamed) is used for a court of law (Exodus 21:22), and what is the function of a court if not to sift evidence and make a decision?
A logical extension of Peh-Lamed-Lamed is the related root Peh-Lamed-Heh, meaning a clear separation between two things. Thus, prayer is the soul's yearning to define what truly matters and to ignore the trivialities that often masquerade as essential (Siddur Avodas HaLev).
People always question the need for prayer – does not God know our requirements without being reminded? Of course He does, He knows them better than we do. If prayer was intended only to inform God of our desires and deficiencies, it would be unnecessary. Its true purpose is to raise the level of supplicants by helping them develop their true perceptions of life so that they can become worthy of His blessing.
This is the function of the evaluation, decision-making process of Tefillah, prayer. The Hebrew verb for prayer is mitpahlel; it is a reflexive word, meaning that the subject acts upon himself. Prayer is a process of self-evaluation, self-judgement; a process of removing oneself from the tumult of life to a little corner of truth and refastening the bonds that tie one to the purpose of life.