What does this symbol mean? (looks like a 1 with double vertical line)

Solution 1:

It's the characteristic function (or indicator function) of the set in the subscript.

$$\mathbb 1_A(x) = \begin{cases} 1\,, & x\in A \\ 0\,, & x\notin A\end{cases}.$$

Solution 2:

It is the indicator function.