Learn Russian: Где машина? Её нет дома. - Where is the car? It is not at home.

In Russian, all nouns have a gender. The word for car, машина, ends in -а, making it a feminine noun. Because of this, Russian refers to the car as "she" (она) rather than "it". It becomes её here because of the grammar in the second sentence.

Why do we use the Genitive form её instead of the basic form она?

The word нет (when used to mean "is not present" or "does not exist") forces the thing that is missing to be in the Genitive case. The Genitive form of она is её. Think of it literally as "Of her there is not at home."

Is this the same её that we use to say "her car"?

Yes! The possessive word for "her" (as in "her house") is exactly the same as the Genitive form of "she". So её does double duty in Russian depending on the context. Here, it just means "her/it".

Why is the word for home дома instead of just дом?

Дом is the basic noun for "house". However, when you want to say someone or something is "at home", you use the special location word дома. It acts as a fixed adverb to answer the question "where?".