If divergence refers to a vector field flowing towards or away from a point, curl refers to that vector field flowing around a point, either clockwise or counter clockwise.
It is defined for two and three dimensions.

Positive curl means that the field is flowing counter-clockwise around a point. Negative curl means that it's flowing clockwise, and zero curl means it does not tend to flow around that point at all.

The definition for the curl is different for 2 and 3D, in 2 dimensions it is the determinant of the matrix formed by the gradient vector on the first column and the components of the vector of this function on the second column, while 3D curl is the cross product of the gradient and the vector function , so we have