Countability is a grammatical feature of nouns. For example, English nouns can be described as countable or uncountable. This is a distinction which native speakers are normally unaware of, but anyone who has studied or taught English as a foreign language will have come across the concept. To put it in very simple terms, countable nouns denote things that can be counted, i.e. objects, persons or events of which it is possible to distinguish and enumerate one or more separate examples or instances. Consequently, countable nouns can occur in the singular or plural. Countable nouns in English have distinct singular and plural forms, except for a handful whose plural form happens to be identical to the singular for etymological reasons (e.g. fish, sheep, aircraft etc.). In contrast to these countable nouns, English also has uncountable nouns, which denote things that cannot be counted because they consist of an amorphous continuum, typically substances and materials, such as milk, gold, butter, bread etc., but also abstract concepts, such as courage, boredom, compassion etc., and words denoting actions, such as the names of sports, academic subjects and languages. If you think about it, you cannot normally make these nouns plural and you can’t count *one courage, *two courages, *three courages. Hence the name uncountable.
As stated above, this is a distinction in English which native speakers deal with instinctively and unconsciously, so mostly never stop to think about. For learners of English, it would be simple enough to deal with the distinction if it were the case that each noun in the language fell into one of the two categories. But the problem is that the same noun can shift categories. So, for example, the word coffee is uncountable when it refers to the substance, as in I like coffee, Coffee is one of Brazil’s most important exports, but countable when it refers to either a cup of coffee, as in Would you like a coffee?, I’ve had three coffees already this morning, or a variety of coffee: Java is a coffee grown in Indonesia, The store sells coffees from around the world. This semantic shift from uncountable substance to countable portion or variety is a regular pattern both in English and Portuguese, so just as it is perfectly correct in English to order two waters, please you can also ask for duas águas in Portuguese.
But countability in English has a more complex side to it. Consider the difference in meaning between It’s an interesting work vs. It’s interesting work; I bought a paper vs. I bought some paper; You got me out of a jam vs. We’re out of jam; He dropped the football vs. He dropped football; I like chickens vs. I like chicken. These are just a few examples of the large number of nouns in English whose meaning changes, sometimes slightly, sometimes radically, depending on whether they are used countably or uncountably.
With these major differences of meaning, it’s obviously important when a noun is mentioned for the first time to signal to the listener or reader whether it is to be understood in its countable or uncountable sense. English does this by judicious use of the definite and indefinite articles (the and a(n) respectively). Normally, when a new noun is mentioned for the first time, it will be indefinite, i.e. its exact identity not yet specified. If it’s not indefinite the first time it’s mentioned, it’s because its referent, and therefore its countability, is assumed to be already known to speaker and listener (e.g. the paper in Did you see that ad in the paper?). When indefinite, plural countable nouns and (singular) uncountable nouns are either used with no determiner at all (e.g. I like apples/coffee) or if the context requires, the determiner some (e.g. I bought some apples/coffee), which may be replaced by any in negative sentences and questions. A singular countable noun is preceded by the indefinite article a(n). This rule allows us to distinguish between I bought (some) paper and I bought a paper. In other words, the indefinite article actually has two functions in English grammar: first, to indicate indefiniteness, and second, to indicate countability. It follows that you cannot put a(n) before an uncountable noun, because by doing so, you will make it countable and that will very probably change its meaning. Consider once more It’s interesting work vs. It’s an interesting work.
There are some important differences in the way countability works in Portuguese which can lead to mistakes, both by English learners of Portuguese and by Brazilian learners of English. First of all, there are very few cases in Portuguese where countability radically changes the meaning of the same word as can happen in English (cf. jam vs. a jam; lace vs. a lace; gear vs. a gear etc.) Secondly, a large number of words whose equivalents in English are uncountable can also be used countably in Portuguese, usually necessitating a different translation, e.g. trabalho ‘work’ (um trabalho, trabalhos), música ‘music’ (uma música, músicas), comida ‘food’ (uma comida, comidas), besteira ‘stupidity’ (uma besteira, besteiras), violência ‘violence’ (uma violência, violências) etc. Thirdly, the rules for article use are different in Portuguese, especially as regards the indefinite article um(a). There is not the same requirement to use an indefinite article to introduce a new countable noun and so there are a number of cases where Portuguese dispenses with the article whereas English requires it, such as expressions of profession or religion after ser ‘to be’ (Ele é ator vs. He’s an actor); after verbs of becoming and transforming (A casa virou museu vs. The house has become a museum; Transformamos o quarto de hóspedes em escritório vs. We’ve turned the guest room into an office); after como when it means ‘as’ (Ele trabalha como garçom vs. He works as a waiter); after the preposition sem (Saí de casa sem guarda-chuva vs. I came out without an umbrella); in appositional phrases (Fernanda Torres, atriz brasileira vs. Fernanda Torres, a Brazilian actress); and when the noun is used in a more generic sense (Eles têm cachorro vs. They have a dog). On the other hand, Portuguese grammar requires the insertion of an indefinite article when an otherwise uncountable noun is qualified by an adjective, whereas in English the indefinite article cannot precede an uncountable noun under any circumstances (e.g. Enfrentamos um trânsito intenso vs. We hit heavy traffic; Está um tempo horrível hoje vs. It’s horrible weather today; Ela fala um inglês perfeito vs. She speaks perfect English; Eles têm uma paciência incrível vs. They have incredible patience, etc.). In addition, in spoken Portuguese, um(a) can be used before an uncountable to mean ‘some’ (e.g. Meu avô me deixou um dinheiro vs. My grandfather left me some money; Quer um leite no café? vs. Would you like some milk in your coffee? Vou fazer um arroz para nós vs. I’ll make us some rice etc.). Note that in examples such as the last, the article becomes obligatory if the noun is further qualified by an adjective (e.g. como fazer um arroz gostoso e soltinho vs. how to make delicious fluffy rice).
But perhaps the most striking feature of countability in the spoken language of Brazil is that otherwise countable nouns are used uncountably to denote a generic or indefinite plurality, so eu gosto de maçã translates ‘I like apples’ and comprei maçã means ‘I bought (some) apples’. ‘I bought an apple’ would be comprei uma maçã with the indefinite article, and the plural form maçãs would have to be used after a specific number or individualizing quantifier such as várias ‘several’. It is possible to combine this type of uncountable noun with the collective quantifiers muito and pouco, however, so you say for example como muita maçã ‘I eat a lot of apples’. This type of uncountable noun with generic plural meaning can also occur as the subject of a general statement, e.g. Maçã faz bem à saúde ‘Apples are good for you’; Criança gosta de doce ‘Children like sweets’. In more formal written language, these sentences would be expressed as A maçã faz or As maçãs fazem bem à saúde and A criança gosta or As crianças gostam de doces, observing the formal rule that the definite article must accompany a noun used in a general sense.
This kind of uncountable with plural meaning is the norm in the spoken language and also much used in less formal forms of writing. It leads to a good deal of fluctuation between the use of singular and plural in certain types of context. For example, while the “correct” formal expression is escovar os dentes ‘to brush your teeth’, in informal language people say escovar o dente. This in turn leads to variation between the more “correct” term escova de dentes ‘toothbrush’ and the more commonly used escova de dente.