There are a few things here to which I wanted to respond.
As an atheist, I see two possible answers to this question. The first is, simply, "nothing". We are accidents of evolution, there is no 'purpose' or 'goal' in the universe in having us exist. There is no "inherent" value to our lives, if by that you mean a value determined from or derived from something outside of ourselves.
What I meant was, now that we're here, what difference does it make? I suppose to answer my own question, I would have to look at scale. On a grand scale, each individual human life means next to nothing, and the universe doesn't care whether we live or die. On a smaller scale, when it comes to who we are in society and how we affect the lives of others, our lives matter more. To our friends and loved ones, we matter a great deal. Logically speaking, one cannot compare the properties of the whole to the properties of the components, so to ask if the universe has a purpose for us is the fallacy of composition.
The other answer is "The inherent value of our lives is determined or defined by us". Lacking any external source from which to derive our value, it is up to us to define it.
Do you mean us as individuals in terms of self-determination? Or us as a society or species?
From a very pragmatic viewpoint, we can argue that evolution is a natural process, of which we are a result. We exist because we have survived and evolved to become who we are; and our value consists of continuing simply to exist. Failure of humanity to exist would indicate that we have failed from an evolutionary viewpoint, and thus no longer have value.
From a more philosophical viewpoint (and this is the viewpoint towards which I tend), our "value" is determined by ourselves. There isn't any "inherent" or "intrinsic" value, but rather we determine for ourselves what value we have.
For me, as a Humanist, my "value" is determined essentially by my ability to contribute in a positive manner to humanity. Whether this be helping individuals, or large groups, it's all got 'value'. The more people I'm able to help, the greater the value of my life.
So then would you say that value is determined by contributing to the continued existence of humanity? Also, I know you've probably already mentioned this, but what kind of work do you do in helping others?
Others, I'm sure, will have other criteria. I don't think there can be any 'absolute' answer to this question, there is no one 'right' answer; it will vary from person to person, from case to case. Another answer, already given above, is that our ability to ask that question is what gives us value; no other living creature on the planet asks that question, it is what sets us apart.
True, but humans are also set apart by our unique ability to destroy all life on the planet, which isn't a very positive distinction.
The only answer that I disagree with is the "our lives have no value" one; in the end, from a very logical perspective, it may be true -- but it results in a life of pointless desperation. If it is true that our lives have no purpose, then it can't possibly hurt to create our own purpose...and thereby make our own lives, and the lives of others, more happy and fulfilling during our brief sojourn on this mortal coil.
This is where I struggle the most. It's very subjective, but I feel I have to diminish my own value to avoid becoming a selfish undeserving bastard. I know that, logically speaking, this is precisely what prevents me from contributing to humanity in a positive manner. It's a vicious cycle, and part of the reason I initially posed this question. I've been struggling to break out of this mindset, to no avail. I can't allow myself a moment of happiness or fulfillment.
My friends tell me I'm worth something to them. I have a hard time believing what I hear.