Meaning of $|w| ≡ 2 \mod 3$ I'm new to formal language and automata theory and I was left alone with this exercise. The task is to define a formal grammar for given language. 

$Σ \in \{a,b\}$  

$L = \{ w \in Σ^*\, |\, |w| \equiv 2 \mod 3 \} $

I already solved tasks of that kind, but now i struggle to understand what $|w| \equiv 2 \mod 3$ means. $|w|$ means the length of $w$ right? Does $\equiv 2 \mod 3$ mean that $|w|$ should be $2$ (because 2 modulo 3 is 2)?
Yes, $|w|$ is the length of $w$.

So $|w| \equiv 2 \mod 3$ means that the length of w divided by three should have the remainder 2. It should be from the set $\{2, 5, 8, \dots\}$.