How does the tensor product of matrices of dimension $2$ act on $\mathbb{C}^{2^n}$?

Question

Consider the vector space $\mathbb{C}^{2^n}$. I recently read in a book about Clifford algebras that its endomorphisms are given by $\mbox{End}(\mathbb{C}^{2^n})=M_2(\mathbb{C}) \bigotimes ...\bigotimes M_2(\mathbb{C})$ where the number of factors in the tensor product is $n$. Can you tell me what this identification is? How does a tensor act on $\mathbb{C}^{2^n}$?