The implication of the quote is to deny a sense of transcendence amongst individuals. In reconfiguring reality as one where nothing exists except through human consciousness or action, the logical result of this is suggesting that there can be no totalizing force that supersedes individual action. Hence, there can be no Divinity or sense of spirituality which guides our action because "nothing exists except through human consciousness." For the Party in Orwell's work, this consolidates their own sense of power. If individuals acquiesce to the idea of sacrificing totalizing forces, then they must accept that human made constructs of power are all that exists, meaning the force which is in power is what exists. Orwell constructs this quote to suggest what happens in any political or social setting where singular notions of the good become power based exercises in establishing and tightening control over others.
If you think about it, how do we know that anything exists? The only way I know anything is through my own consciousness. I can not know anything except through my physical senses and my ability to think and imagine.
That is true for me, but also for every other human being on earth.
So you can argue at least that nothing would exist if there were nothing around to perceive it -- sort of like the old saying "if a tree falls in the forest and no one is around to hear it, does it make a sound?"
Or, as O'Brien says, the earth couldn't have existed before people since there would have been nothing to perceive it before people existed (since he would not believe in God).
I hope that helps.