What does it mean to pray?

The root of word of prayer means "to entreat" -- though in its modern usage the word can also mean communion or meditation. There are only three types of prayer: invocation, incantation, or meditation.

Invocation is from "to invoke," meaning a voiced supplication to a higher power; for instance: the Invocation of the Muse, as found in Greek plays. It is a voiced entreaty.

An incantation is similar to an invocation, only it's meant to be sung or chanted. There is more importance placed on exact wording, since the power is found within the spoken word itself and the rhythm and rhyming of the words is magical. A "hymn" is the term for a Judeo-Christian liturgical incantation. A hymn invokes, through rhythm and rhyme, the presence of the Christian Muse, the Holy Ghost.

Meditation is the least recognized form of prayer: in fact, meditation is normally relegated to Oriental religions -- although, to be fair, Buddhism and Shintoism also employ chanting and ritual prayer. Because of this, meditation is usually called "silent prayer" in Western religions. Of course, silent prayer is not exactly synonymous with Eastern meditation. Eastern meditation is much more an introspective action and focuses on self-mastery. However, I would argue that Christian meditation possesses a varied form of the same: soul-searching, repentance, and submission to a higher power.