neccesary condition for a conservative field

Question

$T(x,y)=(T_1(x,y),T_2(x,y))$ be a vector field defined on an open set $M\subset \mathbb{R}^2$ with continuous partial derivatives of $T_{1,2}$. Can we somehow visualize what does the necessary condition fot $T$ to be conservative $$\frac {\partial T_1}{\partial y}=\frac {\partial T_2}{\partial x}$$ actually mean?