We will give a simplified and a direct proof of a special case of Ratner's theorem on closures of individual orbits of unipotent flows ; namely, the case of orbits of the diagonally embedded unipotent subgroup acting on ${\rm SL}(2,K)/\Gamma _1\times \dots \times {\rm SL}(2,K)/\Gamma _n$, where $K$ is a locally compact field of characteristic $0$ and each $\Gamma _i$ is a cocompact discrete subgroup of ${\rm SL}(2,K)$. This special case of Ratner's theorem plays a crucial role in the proofs of uniform distribution of Heegner points by Vatsal, and Mazur conjecture on Heegner points by C. Cornut ; and their generalizations in their joint work on CM-points and quaternion algebras. We will also deduce the corresponding uniform distribution theorem assuming Ratner's ification of ergodic invariant measures as a consequence of our proof. A purpose of this article is to make the ergodic theoretic results accessible to a wide audience.