I would like to attempt a sketch here of Gurdjieff's approach to our species' purpose in this world, this life. I may later give a more thorough description.
To begin, you need to understand the distinction between involution and evolution, in his terminology. In essence, you can see the distinction in the spiral of a shell. If you travel from the outer rim, down into the centre, then that is involution. Travelling from the tiny centre out and up to the outer rim is evolution.
In Gurdjieff's terminology these words take on added meaning. Involution is where energies from a higher source permeate down to the lower levels. Like sunlight, which comes from the sun and is taken in by plants and then passes through multiple process down the food chain to the lowest layer of complex life. To accomplish this transformation down the levels of life-form hierarchy, vehicles are required - in this case the physical vehicles of each life form, down the chain.
Evolution is the opposite process, where energies are taken up from lower forms and transformed into higher. For example, plants take up water and minerals - small simple animals eat plants - larger, more complex and clever animals eat those on the food chain below them. Humans eat all these and produce poetry, buildings and vast complex systems of interaction.
In it's simplistic form, you get the picture. But in both involutionary and evolutionary processes, mechanisms of transformation are required. The energy is taken from above and below, then processed within a vehicle in unique mechanisms. The vehicle itself is affected and transformed by the very process of transformation it is working upon the energies that pass through it.
Just as a motor vehicle which takes in mineral fuel and is then used for our own purpose - is in itself transformed by the quality and purpose which we put that car to. A sensitive can feel the soul of a car when she steps into it - the purposes and thoughts of its owner.
Next you have to understand Gurdjieff's theory of 'reciprocal maintenance'. In essence it means everything feeds on everything else. All entities of the universe, seen and unseen, feed off, and feed each other - that is how the universe works. All processes within the universe have to draw their energy from that released by other processes. The normal method of this is death. In order for one entity to live and act out it's cosmic purpose, it must feed. For that to happen something else must die. That is reciprocal maintenance.
In order for the highest level of action and purpose, those below it have to die and thus release their energetic essences. In order for the lowest level of action and purpose - the higher ones must also die, and dissolve downwards.
Reciprocal maintenance is the process of transformation which fuels the involutionary and evolutionary flow of the universe.
But death is not the only method of releasing energy for this mutual feeding.
Gurdjieff held that the primary purpose of wars, mass diseases or calamities, where millions die, was to release the necessary energy for major transformations of higher beings. But they take the death-released energy, because they mostly are unable to get higher quality food.
When a person takes higher and lower energy into their 'transformational machine' - their body - and produces with effort a product of higher quality - an energetic enhancement, like something of great beauty or great value to the betterment of all living beings - then that releases a very special energy which is of far greater value to the higher beings who feed on this in their turn.
Thus the purpose of humanity, like all beings, is in the basic level, to die and feed all beings, both high and low. But we have a higher purpose - to transform our own feeding into evolutionary forms. This is of inestimable value to both higher and lower beings. It can be taken instead of our death, in varying degrees of 'death'.
Our 'obligation' therefore, if we wish to rise above the basic level of farmed food, is to transform our life. To create from out of our own vehicle processes, 'products' which reach further along the evolutionary spiral. Not just live a life of eat, procreate, sleep, and die. We have to create higher value in whichever way our vehicle is designed to operate. Each person has their own unique task in the evolutionary spiral.
We have to find what this is and devote all our surplice energy to it.
Gurdjieff went further. He maintained that it is precisely in this evolutionary, transformational process, performed by our physical vehicle, that we are able to create an immortal subtle vehicle - the double, or 'active' astral body.
By transforming energies into higher value, in an active self-aware state, we are able to vivify our astral body to a degree which partakes of the very essence of evolution. And in so doing we have the possibility of evolving it's existence into infinity. That is the natural consequence of self-aware transformations.
For us this means we have to first learn self-awareness. Then we have to identify the specific work of transformation that is our destiny in this life. That is our core 'task'. It could be anything, but each being has cog in the evolutionary purpose of our Endless Creator - each a star in the heavens.
It is not enough to be self-aware. We also have to find and pursue our 'evolutionary tasks'. In the first instance, that means everything we do must become a work of beauty - every attitude a force of knowledge.