Equivalent expression in English: Set Notation $\{0,1\}^K$
In set theory $B^A$ denotes the set of functions from $A$ to $B$. Thus, an element $f\in B^A$ is a function $f:A\rightarrow B$.

In your specific case $\{0,1\}^k$ is the set of functions from the natural number $k$ -- a set with $k$ elements -- to $\{0,1\}$. An element $M\in\{0,1\}^k$ is then a $k$-tuple of zeros and ones, i.e., a binary string of length $k$, as said by Yuval Filmus in a comment.

Note that not any combination of 0's and 1's up to length $k$ is valid, but only those with exact length $k$.