Why does 2 mod 4 = 2?

Mod just means you take the remainder after performing the division. Since 4 goes into 2 zero times, you end up with a remainder of 2.

Modulo is the remainder, not division.

2 / 4 = 0R2
2 % 4 = 2

The sign % is often used for the modulo operator, in lieu of the word mod.

For x % 4, you get the following table (for 1-10)

 x x%4
------
 1  1
 2  2
 3  3
 4  0
 5  1
 6  2
 7  3
 8  0
 9  1
10  2