What does the symbol $\Delta$ stands for?

Question

While studying Landau-Lifshitz equation following term appears,

$-m \times (m \times \Delta m) = \Delta m + |\nabla m|^2 m$

In above equation m is a vector quantity. It will be great if someone can point out what the symbol $\Delta$ here stands for and how these two sides are equal.

Answer 1

By definition, $$ \Delta = \sum_{i=1}^{n} \frac{\partial^{2}}{\partial x_{i}^{2}}. $$

Answer 2

It is the Laplace Operator, or the divergence-of-the-gradient operator (not as catchy, though).