Source : Free On-Line Dictionary of Computing

bound variable
     
        1. A bound variable or {formal argument} in a function
        definition is replaced by the {actual argument} when the
        function is applied.  In the {lambda abstraction}
     
        	\ x . M
     
        x is the bound variable.  However, x is a {free variable} of
        the term M when M is considered on its own.  M is the {scope}
        of the binding of x.
     
        2. In logic a bound variable is a quantified variable.  See
        {quantifier}.