Not understanding modulo I'm not sure if I'm in the right place, but I'll give it a try! I'm very bad with mathematics even though it's pretty interesting. Well, for Java programming we have to use the modulo operator, but I just don't get the modulo it self. I hope any of you would be able to explain in simple words and with an example what it does.
 A: If you mean Modulo operation like "3 mod 2" then this is just the remainder when you divide 3 by 2. 3 divided by 2 is 1 with a remainder of 1, so "3 mod 2" is 1.
In order to understand this, you must first be able to do long division by hand (using calculators doesn't work since you get decimal numbers). If you know long division, then it's really easy to calculate any number modulo any other number (natural numbers only).
For example 4 mod 2 is 0 because 4 is divisible by 2.
16 mod 3 is 1 because 16 divided by 3 is 5 with a remainder of 1. In other words 3 goes into 16 5 times and there is a remainder of 1.
It's all about remainders! Once you get comfortable with the definition you can learn some algebraic rules of manipulating these remainders.
A: Let $a$ > $m$ be integer numbers. Then you have
$$ a = q \cdot m + r $$
where $q$ and $r$ are unique integers (maybe $q=0$), and $r$ is called the remainder. By definition
$$ r = a \mod m $$
or if you prefer $a$ % $m = r$.
An example: $a=7, m = 3$. We have
$$ 7 = 2\cdot 3 + 1 $$
so we see that $7 = 1 \mod 3$.
Hope this helps!
A: When you first learned about division, it might even have been before you learned about fractions. If you are dividing integers ("whole numbers") then instead of writing 
$14 \div 3 = 4\frac{2}{3}$
you can write 
$$14 \div 3 = 4 \text { remainder } 2.$$
The modulo operator is just the function that takes two integers and gives the remainder when the first is divided by the second:
$$14 \mod 3 = 2, \quad$$
The other operator of integer division is usually called $\text{div}$, and $x \text{ div } y$ is defined, as you'd expect, to be the greatest $n$ such that $y \times n \leq x$. So for example $14 \text{ div }3 = 4$. And we can define $\text{mod}$ formally as: 
$$x \mod y := x- (y \times (x \text{ div } y)).$$
Is this clear?
