An anastomosis is defined as a network of streams that both branch out and reconnect. In human body the blood vessels frequently anastomoe at the places where requirement is high.
Simply put anastomosis is the connection of two structures. [A look at the picture below would explain it in detail].
When it occurs between blood vessels it is called circulatory anastomosis. The circulatory anastomosis is further divided into arterial and venous anastomosis. Arterial anastomosis is common around elbow [picture below], palmar arch in the hand, plantar arch in the foot and anastomosis around the knee among others.
The term anastmosis is also used in surgery when a segment of intestine is resected and the two remaining ends are sewn or stapled together. The procedure is called intestinal anastomosis.