What is the meaning of countable and uncountable?

Answer 1

Linguistically, "uncountable" simply means "cannot be counted"; it's often used for things that would be impractical to count -- the number of stars in the sky, the number of grains of sand on a beach, the number of leaves in a forest. (The word "countless" is also used as a synonym.)

There's another meaning in linguistics -- a "count" noun (sometimes but not often called a "countable" noun) is a noun that you can count. You can, for example, count Sandwiches (we have five people coming to lunch so I'll make ten sandwiches), but you can't count milk. (Milk is an example of a "mass noun"; I can't have ten milks. I have to measure milk instead and pour five "quarts of" or ten "glasses of" milk.)

There's also a more technical meaning in mathematics -- a "countable" number is a number that is either finite, or at most as large as the number of natural numbers (0,1,2,3,4,....). Yes, there are infinitely many natural numbers --- but infinity comes in different sizes and some sizes are larger than the size of the infinity of natural numbers. So the number of natural numbers is "countably infinity," while the number of sets of natural numbers is uncountably infinite. But the math gets hard and a little strange at this point.

Answer 2

In grammar, countable nouns refer to things that can be counted individually (e.g. "books"), while uncountable nouns refer to things that cannot be counted individually (e.g. "water"). Countable nouns can be made plural, while uncountable nouns remain the same in both singular and plural forms.