Countable nouns refer to things that can be counted, take plural forms, and use articles like "a" or "an". Uncountable nouns refer to things that cannot be counted, only have a singular form, and use quantities like "some". The document provides examples of countable nouns like "apple" and uncountable nouns like "bread", and explains that "how many" is used to ask about counts while "how much" asks about amounts of uncountables.