During our school education all of us heard math teacher saying: "Division by 0 is not possible" but how many of those teachers bothered to explain why is that true? Well, to understand why division by 0 is not possible let's go with simple examples.

What is multiplication? Multiplication is adding addition. What do I mean by this?

$$5 * 3 = 5 + 5 + 5$$

As you can see, 5 is the quantity of something and 3 is how many times we are adding 5 on each other. Right? That's quite simple.
What is division? Well, Division is oposite from multiplication, this time we subtract numbers backwards.

$$\frac{15}{3} = 15 - 5 - 5 - 5$$

As you can see, we subtracted 3 times number five from original quantity 15.
Now, how to solve this problem:
$$\frac{1}{0} = ?$$

Okay, let's thing of the problem in this way. What if we divide numbers to a very close number to zero such as:

$$\frac{1}{0.1} = 10$$
$$\frac{1}{0.01} = 100$$
$$\frac{1}{0.001} = 1000$$
$$\frac{1}{0.0001} = 10000$$
$$\frac{1}{0.00001} = 100000$$

As we can see, the closer we get to the zero, higher number we get. It's quite logical to assume if we continue like this we will come to infinity:
$$\infty$$

Okay, people would say "So, division by 0 gives Infinity, right?" . Well, not really. Let's see this:

$$\frac{2}{0.1} = 20$$
$$\frac{2}{0.01} = 200$$
$$\frac{2}{0.001} = 2000$$
$$\frac{2}{0.0001} = 20000$$
$$\frac{2}{0.00001} = 200000$$

Do you see what's going on? Once more, we are going to reach infinity and by doing so something odd happens.

$$\frac{1}{0} = \infty \land \frac{2}{0} = \infty \implies 1 = 2$$

What I just wrote means: "If one divided by 0 gives infinity and two divided by 0 gives infinity, that means that one and two are equal".
But we know that's not true, right? One and two are not same. This  works for all numbers, both positive and negative.

Having all of this in mind, it's not hard to  see what division by 0 is not possible, but undefined. It's just not possible to understand to outcome.

You can checkout better explanation here: