The copula is a "linking verb" (Crystal 1991: 84). The most frequently used one in English is probably be and its conjugated forms: am, is, are; was, were; being; been. The function of the copula is to link phrasal constituents of sentences, especially a subject and its predicate. Predicates in English that can be linked to a subject by the copula include:
(1) Noun Phrase: This is a book.
Prepositional Phrase: They are at school.
Verb Phrase: I am walking home.
Adjective Phrase: She is tall.
In the English Creole that I am using for this exercise, only the first two would have a copula, and only one of those uses something that sounds like English is- but more about that in a later installment. The other two would look like this:
(2) Verb Phrase: A wakin hom.
Adjective phrase: Shi tal.
In some varieties of African-American, the first two would also usually not have a linking verb. Note the following from AAVE:
(3) Noun Phrase: This a book.
Prepositional Phrase: They at school.
At some times and places in the past (and sometimes even now) children, especially African American children, who produced sentences like those in (2) and (3) were labeled as cognitively deficient or language-impaired, because the sentences don't contain an identifiable "verb," a thing we deem necessary for complete sentences in English, as in (1) above. Such children have even been placed in Special Education classes, and in fact the Head Start Program was in its earliest years designed to get African American children out of their supposedly language-deficient homes.
But there's a problem, and it's not a minor one. The languages of the world are not all in agreement about what needs or doesn't need to appear in the predicate of a sentence. All languages have predicates, but they can be interestingly and even surprisingly different in terms of what they demand. To give an extreme example, Aymara, a language found mainly in the Andes in the region where Perú, Bolivia, and Chile intersect, demands an accounting of the source of the information presented in the predicate. The source might be personal knowledge (I was a witness), knowledge through language (a witness told me), evidence of some kind that I or someone else saw, a legend or myth about which nobody alive has personal knowledge, or even an admission that no source is forthcoming (I'm just talking for the sake of talking). In English we can say, with impunity, she ate the cheese, without any source of evidence or validity whatsoever. Aymara requires more:
(4) Jupax kis manq'iwa (she ate the cheese, and I saw her do it).
Jupax kis manq'iwa siwa (someone who saw her says that she ate the cheese).
Jupax kis manq'pachawa (I saw evidence-maybe cheese crumbs- that she ate the cheese).
Jupax kis manq'itayna (the old stories say she ate the cheese).
Jupax kis manq'chïxa (maybe she ate the cheese, maybe she didn't, whatever...)
The point is that you have to do something, otherwise the sentence is not grammatical, but this is not required for English except in very special contexts (scientific papers, for example, but certainly not in political discourse!). The further point is that there are plenty of languages around that don't require "verbs" in places where Accepted English requires them. Take the Russian translations of the sentences in (2) and (3):
(5) Eto knyiga (this
Oni v shkole (they
Ona vysokaya (she
There are other, unrelated languages I could ppoint to. For example, here are a couple in Malay-Indonesian:
(6) Ini kuda (this
Kuda ini bagus (this horse
And so on. The point, which I may or may not have taken too long to make, is that languages, including African American ones, differ in what they demand of the predicates of their sentences, and yet they all work as human languages.
No child is "cognitively deficient" just because they might say something like she my teacher. To insist otherwise is simply to be racist.