Let’s look at the following English sentences:

My teacher Tanaka is very strict.

I, the boss, will choose.

You, who are the hero of legend, shall save the kingdom.

In all the above sentences, the copula appears in a clause that is not the main one. In the first and second sentences, the copula doesn’t appear explicitly, but it is present implicitly.

Let’s look at the sentences again, but with the implied copula made explicit in the first two:

My teacher, (who is) Tanaka, is very strict.

I, (who am) the boss, will choose.

You, who are the hero of legend, shall save the kingdom.

In order to render these sentences into Japanese, we’ll need to use the copula in a relative clause, rather than in the main clause. To do that, we’ll need to use a different form of the copula.

The form です (desu) of the copula is actually a shorthand of a another form of the copula.

That other form looks like this:

である (de aru)

Yes, that ある (aru) is the verb of existence ある (aru).

This form of the copula explains why the negative of the copula is ではありません (de wa arimasen) or ではない (de wa nai): these negative forms simply negate あります (arimasu) or ある (aru) and add は (wa) for emphasis.

Let’s look at our example sentences and isolate the relative clauses that contain the copula, along with the noun that the relative clauses modify:

My teacher, (who is) Tanaka

I, (who am) the boss

You, who are the hero of legend

To express these relative clauses in Japanese, we employ である (de aru) as follows:

My teacher, (who is) Tanaka
私の先生である田中
わたしの　せんせいである　たなか

I, (who am) the boss
ボスである私
ボスである　わたし

You, who are the hero of legend
伝説の勇者である貴方
でんせつの　ゆうしゃである　あなた

Now that we’ve created these noun phrases with relative clauses, we can treat them as any noun. We can place は (wa) after them to make them into the topic of the sentence and finally add the predicate:

My teacher, (who is) Tanaka, is very strict.
私の先生である田中はとても厳しい
わたしの　せんせいである　たなかは　とても　きびしい

I, (who am) the boss, will choose.
ボスである私は選ぶ
ボスである　わたしは　えらぶ

You, who are the hero of legend, shall save the kingdom.
伝説の勇者である貴方は王国を救います
でんせつの　ゆうしゃである　あなたは　おうこくを　すくいます

Thus, the である (de aru) form of です (desu) allows employing the Japanese copula in relative clauses.

By the way, since the ある (aru) in である (de aru) is the existence verb, that means that ござる (gozaru) /ございます (gozaimasu), the super-polite form of ある (aru), can be used in the copula as well.

This is commonly done in fiction, especially with characters that are meant to evoke a very old-fashioned Japanese-ness. A notable example of such a character is Shishigami Bang from the BlazBlue series, who always uses でござる (de gozaru) for his copulas.

Bang might say things like:

そうでござる！ (instead of そうです)

結構でござる！
けっこうでござる！ (instead of けっこうです)

面白いでござる！
おもしろいでござる！ (instead of おもしろいです)

This way of speaking sounds exaggerated even to native Japanese speakers, and is meant to characterize Shishigami Bang as eccentric, funny, and extremely old-fashioned.