An ELT Glossary : Countable and Uncountable Nouns

If a noun is used countably, it is seen as an individual item of which there may be more than one example. It can therefore be either singular - Look at that dog! - or plural - Look at those dogs.

When the noun is being used as a singular, countable noun – ie it is singular in the context but can potentially be made plural - the indefinite article is used, while the zero article is used if it is pluralised : John is a teacher/ Helen and John are teachers.

Uncountable nouns also take the zero article : I hate cheese!

Quantifiers can be used with both countable and uncountable nouns. Sometimes the same quantifier is possible with both plural countables and with uncountables - eg some :

I bought some apples(C); I bought some milk. (U)

but others can be used only with either plural countables or uncountables - eg much/many, few/little

He doesn't have much money. (U) / He doesn't have many friends. (C)

Notice that I said “used countably” rather than “is countable”. Although most nouns are generally used either countably or uncountably (so eg piano is usually countable – 
there were two pianos in the room -  and cheese is usually uncountable), many nouns can be used either countably or uncountably if the context is right.  So eg, when types of cheese are being discussed then the noun is used countably : Cheshire, Cheddar and Stilton are three British cheeses.

And if you happened to consider a piano to be a food rather than a musical instrument, you would use it uncountably ( I can't remember where I first heard this example - I suspect it was in a lecture given by Dr. David Crystal round about 1979.):
Baby termite: Mummy I’m hungry. What’s for dinner?
Mummy termite:  Piano. Come into the living room and we’ll eat now.
Baby termite : Oh no! I hate piano!

Another example from Crystal of a concrete noun being used uncountably, this time in his book Making Sense of Grammar (Longman) is a quote he includes from the novel Gormenghast :  "For first and ever foremost he is child."

All the nouns we've looked at so far have been concrete, but the situation becomes particularly complex where abstract nouns are concerned, as many abstract nouns can be used either countably or uncountably with no real change of meaning. Eg : 

The dictionary's content is organised around prefixes, stems, suffixes etc. (U)
The dictionary's contents are organised around prefixes, stems, suffixes etc. (C)

Often it depends mainly on whether the speaker perceives the noun as expressing   as a single generic concept - eg:  I'm not convinced that correction results in much improvement. (U)

or as individual items:  I got her to work on the corrections which I added to her work, and there was a noticeable improvement in her work. (C)

Collocation may also play a part - for example we would talk about the Contents page of a book rather than the *Content page.

A few abstract nouns, however, are not this flexible and can only be used uncountably - eg: information, advice, feedback

See also:  Plural uncountable nouns, anyone?

Recommended Reading
Crystal, D. Making Sense of Grammar, Longman