Nouns that can be counted are called countable nouns; nouns that can't be counted are uncountable nouns. This concept is distinct from grammatical number; hence there are countable singulars, countable plurals, uncountable singulars and uncountable plurals.
In English, countability primarily affects whether a singular noun can take an indefinite article. Contrast "I want a cake" (countable, with an indefinite article) versus "I want cake" (uncountable, with a zero article). Note that the indefinite article can be replaced by other articles or determiners that don't mark countability - "I want the cake", "I want that cake", "I want my cake", etc may all be either countable or uncountable.
In pedagogic grammar, sometimes countability is used as a rule to determine which forms are appropriate. For example, a rule is often given "Use 'there is' with uncountable nouns but 'there are' with countable nouns"; similar rules are often used for determiners "much/many" and "little/few". This "rule" is however, incorrect, though it may seem to work most of the time. A more accurate rule is that "there is" is used with singular nouns, and "there are" with plural nouns, regardless of countability.
NB: An uncountable noun may have a subtly different meaning to its countable equivalent. Since all Teflpedia article titles are singular but articleless, it may be unclear to which concept a particular title refers.