Magnetic scalar and vector potential

[NewtonApple]

Mathematically, Scalar $V_m$ Magnetic Potential is given by

$\overline{H}=∇V_m$​

and Vector Magnetic Potential $\overline{A}$ is given by

$\overline{B}=\overline{∇}X\overline{A}$​

Is there any way I can explain it or define it in words?

 

[maajdl]

The rotational (∇xA) and the irrotational (∇V) parts.