Let us think how division and multiplication works.

If 10/2 = 5 then 2 * 5 = 10
If 10/5 = 2 then 5 * 2 = 10
If 10/0 = ? then 0 * ? = 10

What should be in replace of ? which given the result 10. Here we can not defined it so the answer of 10/0 is undefined.

Explanation

Let you have 10 mangos and want to give then 5 people It is simple division 10/5=2 mangos. Each will get 2 mangos.
Now let us say you have 10 manges and wan to give them zero people. How many mangos will each person get?. It shows that dividing 10 mangos among zero people is impossible. Therefore divide 10 by zero not defined or undefined.

Difference between undefined and infinity.

Mostly people are confused about undefined and infinity.

Undefined

Which is not defined mean that is which never solve. i.e. 10/0

Infinity

Which is not finite that is never end. Example 10/3 = 0.333…

Many of us think that 10/0 equals infinity. But 10/0 does not equal infinity, 10 divide by 0 is not defined. If you have 1/x, you can say that as x approaches zero (x -> 0), 1/x goes to infinity (1/x -> ∞). x approaches zero does not mean x = 0, ∞ is just a symbol for some very large number.