Surfing this site, I have often seen many functions and expressions involving $\bmod$ and I have no clue about its meaning. What does that $\bmod$ mean?
Let $a,b$ be integers and let $m \neq 0$ be an integer. The integer $a$ is said to be congruent to $b$ modulo $m$ if there is some integer $q$ such that $a-b = qm$. Thus that $a$ is congruent to $b$ modulo $m$ means that $m$ divides $a-b$. In this case, we write $a \equiv b \mod m$.
This notation is due to K. F. Gauss. You can find it in Gauss's book Disquisition Arithmeticae.
It depends on the context. The usual one is with an "equivalent to" sign $\equiv$: for example, $26\equiv5\;(\!\!\!\!\mod3)$, which is read "$26$ is congruent (or equivalent) to $5$ modulo $3$", and means that $26$ and $5$ differ by a multiple of $3$. Generally, $m\equiv n\;(\!\!\!\!\mod k)$ means that $m$ and $n$ differ by an integer multiple of $k$. Here it is written with parentheses, which is the traditional way that I prefer; but you will often see it without parentheses, which is easier to write in LaTex: $26\equiv5\mod3$.
It is a reimander calculation In the standard format mod(8,4) equals 0 because there is no reimander in 8/4 but for mod(8,6) equals 2 because there is a reimander. It's just the first number divided by the second and the reimander that comes from it.
Modular Arithmetic is a topic in number theory that deals with division of numbers and their remainders (but not restricted to this). I encourage you to read more about it online here.
As an example $20 \equiv0 \ (mod\ 2) $ because 20 does not leave a remainder when divided by 2. It has very interesting applications in the field of cryptography and internet security.