What exactly is a "Hail Mary"? The practice of a saying a "Hail Mary" is often referred to in colloquial speech, sometimes as a way to caricaturize Catholics. References to the practice instantly conjure up images of Catholicism, priests, and confessionals.

However, beyond these references with my Protestant background I don't actually know much about the practice. I don't even have the vocabulary to properly ask this question. What should a non-Catholic like myself understand about the practice? Where did it originate and what is the purpose? Do other traditions employ such a ritual? Is it fair to call them a ritual?

Edit: If it's simply a prayer, what is the purpose of repeating it more than once? At least the pop-culture references often involve saying "so-many" Hail Mary's in the sense of more being somehow better.
The Hail Mary is simply a prayer. It happens to be recited 53 times during the course of praying the rosary. It is said in place of the psalms for the illiterate.  Since there are 150 or so psalms and traditionally the Rosary is split up into 15 decades to mediate on different events in the lives or Jesus and Mary, each decade consists of 10 Hail Mary prayers. 

Because the purpose is contemplating the life of Jesus and the original purpose was about as far as illiterate medieval's could grasp.  It was certainly a good prayer, shouldn't be construed with any biblical injunction on vain repetition - so long as there is no vanity involved. 

Numbers of prayers are also often assigned by priests as penance during confession.  As far as I know, this is a relatively modern practice (1900's and later).  Easy (and private) penances might bring more people into confession while still conferring the same grace.

Personally, I pray the Rosary every day.  Sometimes it's not done very well, most of the time it is done in a distracted way - but that's my problem, not a problem with the prayer.

Another thing I do is pray 3 Hail Mary's (This is also known as the "Little Office of Our Lady") before bed, asking for the grace of purity while remembering her as a model of purity.



As far as extra-biblical prayers are concerned, the Our Father is straight out the didache (teaching of the 12 apostles).  So even though that's ancient and the Hail Mary is comparatively modern. Catholics continually pray new prayers and invoke the communion of Saints for intercession. We don't ask Mary to forgive our sins, but we do ask her for protection.

The Hail Mary is one in a collection of Marian Antiphons found in the liturgy of the Hours (Book of Christian Prayer).  

It is also prayed as part of the Angelus (a prayer traditionally prayed at 6:00 AM, Noon, and 6:00 PM).