Countable and uncountable nouns vary from language to language. In some languages, there are no countable nouns (e.g. Japanese). In addition, some nouns that are uncountablet in English may be countable in other languages (e.g. advice).

Countable nouns can be separated into individual units and counted. They usually have both a singular and a plural form. Most English nouns are countable nouns:

one phone, two phones
one dog, three dogs
one shirt, five shirts

However, a few countable nouns only have a plural form in English. Here are a few examples:

clothes
pants
jeans
shorts
pajamas

These are often used with some sort of quantifier, or quantity word, to show how they are counted (e.g. “a pair of” pants, “two pairs of” pants, “some” pants).

Uncountable nouns exist as masses or abstract quantities that cannot be counted. They have no plural form.

Here are some common categories of uncountable nouns. Like all things in English (and language in general), there may be exceptions.

A mass: work, equipment, homework, money, transportation, clothing, luggage, jewelry, traffic
A natural substance: air, ice, water, fire, wood, blood, hair, gold, silver
Food: milk, rice, coffee, bread, sugar, meat, water
An abstract concept: advice, happiness, health, education, research, knowledge, information, time
A game: soccer, tennis, basketball, hockey, football, chess, draughts (checkers in American English)
A disease: diabetes, measles, polio, influenza (flu), malaria, hypothyroidism, arthritis
A subject of study: economics, physics, astronomy, biology, history, statistics
A language: Arabic, Chinese, Spanish, English
An activity (in the “-ing” form): swimming, dancing, reading, smoking, drinking, studying

Some nouns can be both countable and uncountable (the so-called double nouns). For example, if room is an empty space that can be used for a particular purpose, the noun “room” is uncountable. If it is a part of a building that has its own walls, floor and ceiling, the noun “room” is countable. If paper is the thin material that you write and draw on (and that is also used for wrapping and packing things), the noun “paper” is uncountable. If it is an academic article (or a newspaper), the noun “paper” is countable. Iron is a hard strong metal that is used to make steel; in this case, the noun “iron” is uncountable. On the other hand, iron is a tool with a flat metal base that can be heated and used to make clothes smooth. In this case, the noun “iron” is countable. Light is the energy from the sun, a lamp, etc. that makes it possible to see things; in this case, the noun “light” is uncountable. If it is a thing that produces light, especially an electric light, the noun “light” is uncountable. If shelter is a building designed to give protection from bad weather, danger, or attack, the noun “shelter” is countable. If it is a place or situation in which you are protected from bad weather or danger, the noun “shelter” is uncountable. Language is the use by humans of a system of sounds and words to communicate; in this case, the noun “language” is uncountable. It is also the particular form of words and speech that is used by the people of a country, area, or social group; in this case, the noun “language” is countable.

Sources: https://academicguides.waldenu.edu/writingcenter/grammar/nouns

https://dictionary.cambridge.org

https://idioms.thefreedictionary.com

https://www.oxfordlearnersdictionaries.com

https://www.collinsdictionary.com

https://www.macmillandictionary.com

https://www.merriam-webster.com