What does $\text{mod}\ m$ in $a \equiv b (\text{mod}\ m)$ means

Question

I am trying to do example 3.6 from this http://www.cs.fsu.edu/~lacher/courses/MAD3105/lectures/s1_3equivrel.pdf script, but I am not sure what does $(\text{mod}\ m)$ means.

Can somebody explain it to me. Thanks.

Answer 1

$m\mid a-b$ as a whole meaning of $a\equiv b$ mod (m)

Answer 2

a= k*m + b ; b is the rest of the euclidian division of a by m