What is a Mezzuzza? I hope I spelled it right. What is it for in the Jewish faith?

A Mezuzah (מזוזה - 'correct' spelling is impossible except in Hebrew, so don't worry about it) is a piece of parchment (from a kosher animal)with the Hebrew text from Deuteronomy 6:4-9 & 11:13-21 written using a quill, black ink (not just any), in a special manner or writing, and are on the right-hand side of the doorway from which the room is most often entered on the upper third of the doorpost - closets not counting as rooms and bathrooms being considered improper to place them.

They are tilted because two famous Rabbinic opinions argued over if they should be horizontal or vertical, but in order to demonstrate the importance of peace at home, compromised to make it diagonal.

What it's for is to fulfill the commandment that says to write "these words", the words from Deuteronomy 6:4-9 & 11:13-21, on your (to Jews) doorposts - this commandment is not considered any more or less important then any of the others (not counting the 3 unbreachable ones).

There are numerous other complicated details involving a legitimate Mezuzah, such as inclusion of "Shadai" and "Cozu bmuchsaz cozu" in precise placements on the back of the parchment, the requirement to have the text examined for any defects twice in every 7 year span, the differences in rules when placed in a rented apartment, house, or Synagogue etc. Message me if you'd like these aspects explained, though it can be phenomenally complicated.

You may want to read these passages from the Bible:

Deuteronomy 6:9, 11:19.

There's this passage about putting the words of God's commandments on our door posts. A mezuzah is a small ornamental container that holds the scrolls containing these scriptures. The mezuzah is fastned do the door post. Jewish people have these on their front door entrances so that they can kiss it every time they enter or leave their home (usually they kiss their fingertips and touch the mezuzah). Jewish people see God and God's Word as being one and the same, so by keeping the scripture there where they see it and can celebrate it every time they enter or leave the house, it helps us to feel more closely connected to God.

http://www.jewfaq.org/signs.htm

Mezuzah

And you shall write [the words that I command you today] on the doorposts of your house and on your gates. -Deuteronomy 6:9, 11:19

On the doorposts of traditional Jewish homes (and many not-so-traditional homes!), you will find a small case like the one pictured at left. This case is commonly known as a mezuzah (Heb.: doorpost), because it is placed upon the doorposts of the house. The mezuzah is not, as some suppose, a good-luck charm, nor does it have any connection with the lamb's blood placed on the doorposts in Egypt. Rather, it is a constant reminder of G-d's presence and G-d's mitzvot.

In addition to some of these answers, one of the prayers contained within a mezuzzah (which, btw, can be put on all doors with the exception of the bathrooms, although most non-Orthodox Jews only put one on their outdoor doorpost) is the Sh'ma: Hear O Israel, the Lord is our G-d, the Lord is One (Sh'ma Yisroel, Adonai Elohenu, Adonai Echad). This prayer reminds us of Judaism's core - the belief in one G-d.

A literal fulfillment of the law to "write the law on your doorposts."

Deuteronomy 6:9 "You shall write them on the doorposts of your house and on your gates."

Here is some information about the Mezuzah.

http://www.judaica-guide.com/mezuzah/

An ornament - either around you neck or on a doorpost - with a passage from Deuteronomy.

they contain the ten commandments written by a kosher scribe on a rolled up scroll.