some questions on spin group

Question

The spin group of an inner product space $V$ is defined in terms of the Clifford algebra of $V$, which is spanned by products of vectors in $V$. Does any vector in $V$ correspond to a reflection in the normal sense? How can we explain the relation $\left<u, v\right> + \left<v, u\right> = 2g(u, v)$ in the definition of the Clifford algebra geometrically?