The Free On-line Dictionary of Computing (30 December 2018):

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.