Definition:

A mezuzah is a small case containing the words of the Shema.

‘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

A mezuzah is affixed to the doorpost of a Jewish home. A mezuzah is a small case containing the words of the Shema. The mitzvah (commandment) to place mezuzot on the doorposts is derived from Deut. 6:4-9, a passage commonly known as the Shema. The Shema is a reminder to keep in our minds and hearts the first line and central premise of the Shema, ‘Hear O Israel, the Eternal is our God, the Eternal alone.’  The commandment to do this involves writing them on the doorposts. The words of the Shema are written on a tiny scroll of parchment, along with the words of a companion passage, Deut. 11:13-21. On the back of the scroll, a name of God, Shaddai is written. The scroll is then rolled up and placed in the case, so that the first letter of the Name (the letter Shin) is visible, or, more commonly, the letter Shin is written on the outside of the case. Mezuzah cases tend to be beautifully decorated in a variety of styles and can be bought at Judaica shops or crafted at home.

The scroll must be handwritten without any error and placed in the case to fulfil the mitzvah. It is commonplace for gift shops to sell cases without scrolls, or with mechanically printed scrolls as properly written scrolls can be costly. According to traditional authorities, mechanically printed scrolls do not fulfil the mitzvah of the mezuzah and certainly nor does an empty case.

The case and scroll are then nailed or affixed at an angle to the right side doorpost as the building is entered with a small ceremony called Chanukkat Ha-Bayit (dedication of the house) This is the same word as Chanukkah, the holiday celebrating the rededication of the Temple. A brief blessing is recited.
The mezuzah is affixed at an angle as a compromise because the rabbis could not decide whether it should be placed horizontally or vertically. A mezuzah serves as a reminder of God’s presence, connection to Jewish tradition and the mitzvot contained in the Shema.

Unless you know that Jews will be moving into your home after you, it is appropriate to remove a mezuzah when you move, and recommended in case the subsequent residents treat it with disrespect.