Learn Russian: У русских есть отчество.

In Russian, the most common way to say "to have" doesn't use a verb like English does. Instead, you use the preposition У (which roughly means "by" or "at"), followed by the owner, then the word есть (is/exists), and finally the thing being owned. Literally, this sentence says "By Russians there is a patronymic."

What case is the word русских in?

It is in the genitive case. The preposition У always requires the genitive case. Because we are talking about Russians in the plural, русских is the plural genitive form.

Why does русских look like an adjective rather than a normal noun?

The word for a Russian person, русский, is actually an adjective used as a noun. It changes its endings exactly like an adjective would. In the plural genitive, adjectives typically end in -их or -ых, giving us русских.

What case is отчество in?

It is in the nominative case (the dictionary form). In the "У ... есть ..." structure, the thing that is owned is actually the grammatical subject of the sentence, so it stays in the nominative case.

What exactly is an отчество?