Many of us spend our lives wondering about this... Why were we born? What is the purpose of our lives? Everything in this universe happened for a reason(that is to say, if you don't wonder about this, you are missing something).
To make my point, we will have to go back to when the world started(or ended the last time). The universe constricted to a single point. But then, the existence of a point depends on the observer's proximity with it. If we soar deeper and deeper into the sub-particles and sub-sub particles, internal disturbances and collisions can be observed. From these, sound waves were generated. These sound waves were of different amplitudes, phases and frequencies. They rearranged themselves into a single universal frequency(that of "om", after all there was a reason "om" was selected to be "om"!) And from then on, to how the world is today; all we have been witnessing as the most unmistakably prominent, time and again prompted(by nature itself) and usually neglected aspect of nature, is its tendency towards stability. From chemistry to maths, physics, biology and almost every other science that exists literally screams out that stability is the most basic objective of every single atom in this universe. And more than often, we fail to implement it to the finer parts of life. Shouldn't we take stability a little more seriously? Aren't we made up of atoms? The sole purpose of each and every living/non-living thing in this universe is to attain stability. If we look at our routines a little more closely, we can see that we actually do follow it! Sleep, is a kind of stability(not that the ultimate aim of our lives is to sleep :P). Peace, is a kind of stability. Most of us involve themselves into a hobby for mental peace and stability. Many of us meditate, for similar reasons. I am a writer and that is what gives me peace, stability.
Similarly, everyone was born with a purpose, something that would help him/her attain stability, peace. If you still can't figure out, have patience. It is just a matter of time. Till then, let us concentrate on the common purpose of each and every human being, that is to make peace (at least)within the human race.
To know the purpose of life one must read Quran.