The answer is so simple that it seems stupid - to live.
Thats it, we are here to live.
But it asks a further question - to live but how?
Here I need to separate humans from other living beings (because as observed humans are more of a deciding factor on other living beings "how" also).

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We see that only some people know this how.
So I"ll take two examples from history, where defintely everyone will agree, the subjects knew why and how.
(These two examples suffer from a huge problem, they are both famous people.
But I take them as everyone can relate easily to them.
These people did not do what they did to become famous.
History made them famous. They did what they did because of their "why".)

Mother Teresa - She was born in Macedonia (formerly a part of Yugoslavia).
She became a nun over there. After that she had a transfer to India for some years on a normal rotation basis.
She used to teach in Calcutta to poor children.
Then she realised that she wants to do something for poor.
She started her own missionary and devoted her entire life to taking care of the poor and downtrodden.
That became her "why". "How" was by starting the missionary and doing whatever she could do.

Issac Newton - He postulated the mechanics theories and the famous law of gravity.
In the midst, he (re)discovered the field of calculus.
Here also he could safely say at the end of his life that his "why" was to write and prove theories. "How" was by using maths and logic.

In both of these examples, along with the basic "to live", these people added more to their "why" and the "how" automatically came up.

Whats so special about these people? Thousands had seen poor and downtrodden and thousands had seen apples fall.

In first case, why did she not go back after her stipulated time? Why did she choose to stay?
Because it moved her to help people. And was she just the right person at the right place at the right time? Far from it.
She spent some part of her life "living it".
What she saw next was that she was in a position to help, in a position to improve.

In the second case the person was in his chosen field, he liked science and maths.
He had all the basic tools ready for him.
He observed something, did not understand it, stuck to it and finally found the solution.

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These two examples fill up most of the cases of "why". What I understand from them is -

1. Either you are already in your chosen field of your liking and prepared to develop more in it,
 which means doing something better/different in the field. (Newton)
2. Or you go around, meet all sorts of people, see where and what you think you can do something and then do it. (Teresa)

Further cases
If I meet a trader whose aim in life is making money, I"ll totally agree with him. He has a "why".

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Now we find some people who in the very start of their lives know their "why" and "how".
Everyone has heard about children wanting to become pilots or joining army or cricket and chess players or musicians
who decide early and then go on and achieve their goals.
Their goals become their "why".
But if someone looks deeper, these people would not even know what a pilot or army or chess or music means
unless there is some huge influence in their lives.
Someone will have a dedicated mentor who will provide the basic tools and basic knowledge and
that excites the child so much that he makes it his "why" also.
If a child of a doctor wants to become a doctor, he has decided because of this influence.
Or else he learns about his field pretty early and is excited about it.

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For the rest, its a constant search.
But a search for what. There are 2 ways to search
1. Search for "why" followed by search for "how".
2. Search for "what".

In the first case we keep on searching for "why" which is not very fruitful.
In the second case we search for "what".
This what is what do I find interesting, what am I passionate about, what I can do to make life better. The "why" in this case automatically comes.

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Next how to find what I find interesting.
Here taking the example of a doctor and his child, his child has found an interesting field, its already present in his life. He knows about it.
Suppose I decide that whatever I like to do, I have not found it till now and whatever people around me do I don"t find interesting.
In this case if I am serious about extending my why, I"ll meet as many people as possible,
experience as many different situations in life and see what they are doing.
Would I like to do the same or would I like to do something better will automatically come up.
Since I am changing my field of interest, I definitely won"t know much about other fields.
Meeting other people, seeing what they are doing will light up a spark.
I"ll gain more knowledge and will know what to do.

One such example would of Mohandas Gandhi.
He was a barrister but seeing poor condition of people and his own poor treatment in SA, he decided to do something different there,
later came back to India and decided to do the same thing.
If he had continued to stay in India, chances are high he would not have done anything different.

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There is a case of housewives, who are forced to stay at home or willingly stay.
"Right to live" should not be taken away from people.
If they want to pursue something they should be allowed to do so.
And someone who willing stays at home already has a why.
She will stay home, take good care of her children and her family and in her free time pursue some of her fav activities like poetry, painting, cooking etc.

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Lastly its not that everyone will have a simple non-wavering why.
Maybe for someone, first half of his life will have "to live and earn money" and second half will have "to live and do charity".
There is no hard and fast rule that a person need to have some fixed why...

So every person has already a why - "to live", rest its mostly personal choice.
Forcing someone else or even yourself to do something which he/she does not like is definitely not going to help.

Its an individual choice...