Countable nouns refer to things that can be counted, such as dogs, pens, bottles, and coins. They can be singular or plural, and require an article like "a" or "the" when singular. Uncountable nouns refer to substances or abstract concepts that cannot be counted, such as milk, music, or furniture. They are usually treated as singular and do not take an article. Both countable and uncountable nouns can be used with quantifiers like "some" or "any".