$M^k \le 2^r < M^{k+1}$
where $M>1 , k>0$ for some $r$.
It simply tells you that there exists a $2^r$ between $M^k$ and $M^{k+1}$. for example:
if $M=3$, $k=1$ then $M^k = 3, \quad M^{k+1} = 9$ and there exists $4$ and $8$ in between $3$ and $9$. i.e., $2^2$ and $2^3$
Edit: (T.B.)
Let $M \geq 2$ and $k \geq 1$ be integers. How can I prove that there exists an integer $r$ such that $M^{k} \leq 2^r \lt M^{k+1}\quad?$