Applying the Nabla operator to a scalar field $$f$$ results in a vector field (gradient field) with three components. At a point $$(x,y,z)$$ the vector $$\nabla \, f(x,y,z)$$ points in the direction of the largest increase of $$f$$.
Here $$\nabla$$ is the Nabla operator. This is a vector operator with which vectorial derivatives like gradient, divergence or rotation can be formed.
A function depending on three coordinates $$x$$, $$y$$ and $$z$$, which must be differentiable. For example: $$f(x,y,z) = x^2 + 5yz + z$$.