This is taken from Chorin's book on Turbulence, in which he considers a function $u: \mathbb{R}^3 \rightarrow \mathbb{R}^3$, $x,h \in \mathbb{R}^3$, and $t \in \mathbb{R}_{\geq 0 }$. Then we may expand $u(x + h, t)$ in powers of $h$ (up until $O(h^2)$) as follows: $$u(x + h) = u(x) + \frac{1}{2}\xi \times h + D\cdot h$$ where $\xi =$ curl $u$ and $D = \frac{1}{2}(\nabla u + (\nabla u)^T)$ is the deformation matrix.
I have not seen the cross product appear in a Taylor series expansion before, where does this come from and/or is there any geometric reasoning behind it? The book mentions that $\frac{1}{2}\xi$ can be seen as a rotation vector, but this is not immediately obvious. Similarly, why is $D$ called the deformation matrix here? How is $u$ being "deformed" exactly?