A quantifier is a logical operator that specifies how many objects in a domain satisfy a statement or formula. Common quantifiers include universal quantification, meaning for all, and existential quantification, meaning there exists.
In logic, quantification specifies the quantity of specimens in the domain of discourse that satisfy an open formula. The two most common quantifiers mean "for all" and "there exists". For example, in arithmetic, quantifiers allow one to say that the natural numbers go on forever, by writing that for all n (where n is a natural number), there is another number (say, the successor of n) which is one bigger than n.