what is it called when you can't put the words an, a or the infront of a noun?

I think the only words that take no articles (a/an/the) ever are proper nouns ("A Cindy"; "The Canada").

Mass nouns or noncountable nouns such as furniture and data can't be expressed as "A [noun]" but as "A [unit] of [noun]", as in "A piece of furnitune", but "the furniture" works.

Come to think of it, I am coming up with some proper nouns that can take a definite article (the) but they're mostly brand names used in place of generic terms.

I'm not sure if there's any sort of noun that never takes an article or what it would be called.

I don't think there is a term for that. Any noun sounds "right" when you put "a, an, the" in front of it. However, in sentences, by custom, we put an article before some nouns in some uses, but not in others. This is very difficult for ESL students. For instance, we say, the Second World War, the Civil War, but World War II.

I taught my students that if "the, a, an" didn't sound right before a noun, that probably it was not a noun but another part of speech. We don't say "the is," "a think," or "the after."

The grammatical concept you are referring to is called "zero article." It occurs when we omit the indefinite articles "a" or "an," as well as the definite article "the," before a noun.

To determine whether to use an article or not, you need to consider the context and specific rules of English grammar. Here are a few situations where the zero article might be used:

1. General statements: When talking about things in a general or non-specific sense, we often omit articles. For example, "Dogs are loyal animals" or "Cars pollute the environment."

2. Plural and uncountable nouns: Plural and uncountable nouns generally do not require an article. For instance, "Cats are cute" or "Water is essential for life."

3. Nationalities and languages: We usually omit articles when referring to nationalities and languages. For example, "She is American" or "I speak English."

4. Proper nouns: Proper nouns, like people's names, names of places, or company names, do not require articles. For instance, "John is my friend" or "I work for Google."

It's essential to note that there are exceptions and additional rules to consider when using articles in English. Understanding these rules and how they relate to specific contexts will help you use articles correctly in your writing or conversation.