Well, really more inconsequential than you can imagine. Anthony Doerr ponders the Hubble Ultra Deep Field, and urges us to do the same:
So. The Earth is massive enough to hold all of our cities and oceans and creatures in the sway of its gravity. And the sun is massive enough to hold the Earth in the sway of its gravity. But the sun itself is merely a mote in the sway of the gravity of the Milky Way, at the center of which is a vast, concentrated bar of stars, around which the sun swings (carrying along Earth, Mars, Jupiter, Saturn, etc.) every 230 million years or so. Our sun isn’t anywhere near the center; it’s way out on one of the galaxy’s minor arms. We live beyond the suburbs of the Milky Way. We live in Nowheresville.
And not only are we in Nowheresville, Milky Way, the Milky Way itself isn't anything special:
[T]here are enough stars in the universe that if everybody on Earth were charged with naming his or her share, we’d each get to name a trillion and a half of them.
Even that number is still impossibly hard to comprehend—if you named a star every time your heart beat for your whole life, you’d have to live about 375 lifetimes to name your share.
The point of this is, in the grand scheme of things you and I are even less than a speck of dust in the desert. Doerr believes that this ought to give us perspective. That this picture "should probably be in every church". He's probably right, but for the opposite reason he thinks.
We are nothing. Just as the Preacher of Ecclesiastes finds despair in the vanity of the meaningless of life, so much so that he "hated life", so the Hubble Deep Field picture will inevitably force the same conclusion. Except that, as the Preacher discovered, we do have meaning. We do have purpose. We find in the fact that God created all of this for you and me. And we find meaning in being created in His image.
The Deep Field image stands as a testament to life's futility without our Creator. And it stands as a magnificent statement of the wonder of the Being who spoke all that the Hubble could ever see into existence.