In mathematics, the transitive closure of a binary relation R on a set X is the smallest transitive relation on X that contains R.
For example, if X is the set of humans (alive or dead) and R is the relation 'parent of', then the transitive closure of R is the relation "x is an ancestor of y". Or, if X is a set of airports and xRy means "there is a direct flight from airport x to airport y", then the transitive closure of R is the relation "it is possible to fly from x to y in one or more flights."
Reference;
http://en.wikipedia.org/wiki/Transitive_closure
