Intuitive way of describing a conformal distribution

Question

I was wondering if anyone knows a way to describe a conformal distribution in an intuitive way, preferably to someone who doesn't have much previous knowledge of differential geometry. I know that a distribution is a subbundle to the tangent bundle. Given a distribution $\mathcal{S}$ and its complementary distribution $\mathcal{T}$, we can define its second fundamental form as $$B(X,Y)=\frac{1}{2}\mathcal{T}(\nabla_XY+\nabla_YX),$$ where $X,Y$ are smooth sections of $\mathcal{S}$. The distribution $\mathcal{S}$ is conformal if there exists a vector field $V$ is $\mathcal{S}$ such that $$B(X,Y)=g(X,Y)\,\otimes\,V,$$ where $g$ is the Riemannian metric. What does this mean, in practice?