What does this modulo operator actually do?

Answer 1

In simple words, a%b gives the remainder when a is divided by b

Most students are taught that "Dividend = Divisor * Quotient + Remainder"
In more sophisticated language, this is the Division Algorithm : For any integers a and b such that b is non-zero, there exist unique integers q and r such that a = b*q + r where 0<=r<b

So a%b gives r

For example, 9 = 2*4 + 1
So 9%2 = 1

Another way to think about it is something like this.
Imagine you have 26 apples and you want to pack them in groups of 7.
26%7 will give you the number of apples left after all the groupings are done.
In this case, you will get 3 groups of 7 apples accounting for 21 apples with 5 apples left. These 5 apples cannot be packed into groups of 7 as 5<7
So 26 = 7*3 + 5
This means 26%7 = 5

Note that making 0 groups is allowed, but the number of remaining apples should be less than that in each group.

Answer 2

I'm not sure what "this" you're referring to, but a modulo operator gives you what is leftover after an integer division. For example:
17 // 5 = 3
because 5 fits into 17 three times (3 * 5 = 15) and
17 % 5 = 2
because that it what is left "unused" after integer division: 17 - (3 * 5) = 2.

Answer 3

It can also help you rotate through certain values. Example:
import turtle
t = turtle.Pen()
colors = ["red", "blue", "yellow", "orange"]
for x in range (100):
t.pencolor(colors[x%4])
t.left(90)
t.forward(x)

As you can see, the modulo operator is used in this for loop and is rotating through the different colors in the variable colors. It is rotating because as x increases, the remainder changes. For example: when x is equal to 4 the remainder is 0 because 4%4 is 0. then when x is equal to 5 the remainder is 1 because 5%4 is 1. The remainder keeps growing larger until it reaches a multiple of 4, which is uncoicidentally the number of colors there are in the variable colors, then the remainder becomes 0 again. Since each colors represent a number, the colors are rotated through. In this case, red is represented by the number 0 so when the remainder of x % 4 is equal to 0 the color changes to red and then to blue when x grows by one and so on.

Answer 4

% or modulo gives you the remainder. Simple example: 3 % 2 = 1 because 2 goes into 3 one time and there's a remainder of 1.