purpose - something set up as an object or end to be attained
Purpose of humans.... Tricky one.
The idea of purpose pretends to the concept of having an objective to fulfill, your purpose of existence would be to attain that objective, or to fill a role in the grander scheme of things, that is, having a continuous purpose to be.
It's hard to squeeze the word 'purpose' in because of causality principles. We can't really tell if an action taken by an individual, a community of individuals, or even the whole humanity, has been taken to attain or to move closer to attaining said objective we're purposed to reach since that said action is just an effect of a previous cause.
Continuing on cause-and-effect, having an Ultimate Purpose
would mean all actions, starting from cellular level and straight up to humanity as a whole would mean that we're walking on an already beaten path (some religious people would call this the Divine Plan). That would entice the idea of an initial cause that somehow magically triggered an insanely long series of effects and causes that ultimately leads to attaining said purpose. That is, if our purpose to be is to attain an end.
If we were to have a let's say 'continuous' purpose to be, well ... What would be my own personal purpose to be ? Or yours ? Or what was your great-great-grandfather's purpose to be ? His actions were decided by his past experiences, desires and intentions. If there was a "purpose" (apart from the universal one, to reproduce) to his existence then how did his actions fulfill this purpose ? Did they at all ? Is our individual purpose fulfilled even if we have no idea what it is ? Then, is it fulfilled by chance ?
Moving on from individuals to the whole humanity, we could be biologically programmed to have a purpose, as a whole. Though again, it is hard to push the word 'purpose' into the equation without adding divinity too.
Let's take bacteria. It lived on the earth for 3 billion years before more complex organisms were formed. Was there a purpose to that ? Later on when algae formed from said bacteria, would you say that its purpose was to enrich the atmosphere with oxygen so more advanced organisms will benefit from it ? Again, a thing like a "Divine Plan" is needed. Oxygen was needed by advanced organisms so algae photosynthesized it. But algae didn't know more advanced organisms would need oxygen, so it couldn't have had purpose in the true sense of the word, from its own point of view, it just evolved in response to the environmental conditions.
My guess would be our purpose is, like any living thing, to reproduce.
To have another purpose than that well ... then something must give you a purpose at creation. If I am a shoemaker I make shoes and I make them with the purpose to sell them or wear them. Tools have purposes. Are we tools ? If we are tools and our creator gave us purpose, the purpose must have been coded in the DNA of the first cell. For all we know tomorrow an alien race will land on Earth and say "Glork". That would trigger a reaction in our brains, turning all of us into slaves, the day after tomorrow we'd be in the alien army fighting their wars or on their lands growing their plants.
But if the first cell appeared by accident then ... The result of an accident doesn't really have any purpose. We're alive, we have to stay alive, we have to reproduce. Isn't it fun being alive ?
Hope that made a little sense at least
edit:spelling and small addition