I'm currently reading An Introduction to Quantum Computing, Without the Physics and on page 10 the following notation is used repeatedly
$$\sum_{j:(jB_q)_{k}=0} $$ or $$\sum_{j:(jB_q)_{k}=1} $$
$jB_q$ is just the notation for the vector containing the binary representation of $j$ on $q$ digits..... so for example $5B_3 = (1,0,1)$ and really it's probably more accurate to think of it as $|101\rangle$ when using the Dirac notation. The k subscript is just the $k$th entry of the vector, so for example $(5B_3)_2=0$. So really I don't know what the colon : means in this case, I assume there is some iterating going on... and not really sure why there is a $0$ or $1$ following an equals sign.
The colon means "such that", just like when you write a set $\{x \in \Omega : P(x)\}$, etc. In words, in the first case the sum is over the indices $j$ such that $(jB_q)_k$ is $0$ (where $q$ and $k$ are fixed a priori, in the context).