The Curl of a Vector field

Essentially, curl is a property exhibited by certain kinds of vector fields. Curl quantifies the net rotational effect of the field. Imagine a fluid flowing in a two dimensional space with certain velocity. Consider a tube that bends back onto itself to be placed in the flow. Now if you imagine that all the fluid except the one present in the tube is frozen, you would see the fluid still under motion due to its inertia. If it happens that the velocity vector of the fluid had non-zero curl, then we would be seeing water gushing around with net momentum inside the tube.

Generally speaking, curl of a vector indicates the presence of tangential components of the vector field that can form a closed loop.

Curl= average tangential component times circumference of the closed loop under consideration.