Source : Free On-Line Dictionary of Computing

free variable
     
        1. A variable referred to in a function, which is not an
        argument of the function.  In {lambda-calculus}, x is a {bound
        variable} in the term M = \ x . T, and a free variable of T.
        We say x is bound in M and free in T.  If T contains a subterm
        \ x . U then x is rebound in this term.  This nested, inner
        binding of x is said to "shadow" the outer binding.
        Occurrences of x in U are free occurrences of the new x.
     
        Variables bound at the top level of a program are technically
        free variables within the terms to which they are bound but
        are often treated specially because they can be compiled as
        fixed addresses.  Similarly, an identifier bound to a
        recursive function is also technically a free variable within
        its own body but is treated specially.
     
        A {closed term} is one containing no free variables.
     
        See also {closure}, {lambda lifting}, {scope}.
     
        2. In {logic}, a variable which is not quantified (see
        {quantifier}).