Count noun
In linguistics, a count noun (also countable noun) is a noun that can be modified by a numeral and that occurs in both singular and plural forms, and that co-occurs with quantificational determiners like every, each, several, etc. A mass noun has none of these properties. It can't be modified by a numeral, occur in singular/plural, or co-occur with quantificational determiners.
Examples
Below are examples of all the properties of count nouns holding for the count noun chair, but not for the mass noun furniture.
Occurrence in plural/singular.
Co-occurrence with count determiners
Some determiners can be used with both mass and count nouns, including "some", "a lot (of)", "no". Others cannot: "few" and "many" are used with count items, "little" and "much" with mass. (On the other hand, "fewer" is reserved for count and "less" for mass (see Fewer vs. less), but "more" is the proper comparative for both "many" and "much".)
Grammatical distinction
The concept of a "mass noun" is a grammatical concept and is not based on the innate nature of the object to which that noun refers. For example, "seven chairs" and "some furniture" could refer to exactly the same objects, with "seven chairs" referring to them as a collection of individual objects but with "some furniture" referring to them as a single undifferentiated unit. However, some abstract phenomena like "fun" and "hope" have properties which make it difficult to refer to them with a count noun.