n graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. The cut-set of the cut is the set of edges whose end points are in different subsets of the partition. Edges are said to be crossing the cut if they are in its cut-set.
Min-Cut: A cut is minimum if the size of the cut is not larger than the size of any other cut.
Max-Cut: A cut is maximum if the size of the cut is not smaller than the size of any other cut.
(Text taken from Wikipedia: http://en.wikipedia.org/wiki/Cut_(graph_theory))