Why 80% of the output is achieved with 20% of the input?

It is not so much a rule as it is an observation...that often times there is uneven distribution with input v.
output.
For example,80% of a business's revenue may come from20% of its customers.
This may be the case where20% of customers are "big ticket" buyers, and the remaining customers are small buyers.
A business may also find that20% of its employees are responsible for80% of a business's achievements.
It is important to note that you might have10% input creating90% output, or20% input creating100% output, and so on.
The issue with regards to strategic planning is not so much what the ratio is but how a business allocates its resources in light of its input / output statistics.
The goal is to focus a business's efforts on the percentage that makes a difference.
For example, where80% of revenues come from20% of customers, a business should focus energy on satisfying those customers more so than satisfying the remaining80% that are not major contributors to the business's bottom line; Or, reward the20% of employees that are responsible for80% of business's achievements.

It is a well-known role called20/80 role

This is what is called Parito principle or the law of vital few (achieving more with less) This principle was named by the Business-management consultant Joseph M.
Jura who named it after the Italian economist Vilfredo Pareto, who observed in1906 that80% of the land in Italy was owned by20% of the population.
The80/20 rule observes that most things have an unequal distribution.
Out of5 things, perhaps1 will be good.
That good thing/idea/person will result in majority of the impact.
The Pareto Principle helps you realize that the majority of results come from a minority of inputs.
Knowing this, if…20% of workers contribute80% of results: Focus on rewarding these employees.20% of bugs contribute80% of crashes: Focus on fixing these bugs first.20% of customers contribute80% of revenue: Focus on satisfying these customers.
it's about quality over quantity.

In my opinion, it depends on the industry and the type of work being considered; in most cases though if your work requires you to put in your own personal touch while performing your tasks; I believe that taking the time to figure out and choose what and how you want to put your effort in, rather than doing as many tasks as possible in the time frame you have, will actually have you reap more positive results and contribute more to reaching your desired outcome.

well known Pareto Principle ,which defines that only20% of people are on top of the food chain when it comes to get the ball rolling.

agree with Fadi Madanat

I do not think so. Because, situation vary business to business.

But, yes it is possible on the strategy planning and implementation.

But in marketing, it is true. Because80% business comes from just20 % of the loyal customers.

Last and most important thing is the observation is very important. Because, business is stand on keen observation and results is the only parameter of it.