We all want to consider ourselves unique. We long for that je ne sais quoi, or that certain something that makes us stand out.
There are many different reasons for this.
Biologically, we have a desire to stand out in order to attract a mate. There’s actual science that backs this up, but I don’t feel like citing, so you’ll just have to take my word for it. :P
Culturally, as American’s, we value our individuality and/or independence above all else. Just look at the hipster revolution. Thanks to the hipsters, it’s suddenly become totally cool to be “uncool” and to literally take a stand against social norms and popular culture.
So yes, we’re hardwired to be different, so long as we’re not too different. But certainly uniqueness isn’t defined by the type of music we listen to or how thick the frames of our fake glasses are, right? 
Which leads us to ask the question:
What makes us unique?
This question could obviously be answered a million different ways, but only one makes the most sense to me. Perhaps, as a writer, I’m biased, but I would say that what makes us unique are the stories we have to tell. Not the fake, made-up stories (though those certainly count for something), but the real-life stories that make up the experiences of our lives.
Now, I don’t believe we are entirely what we have been through, but don’t we all lean a little bit closer, and listen a little more intently to the people who have the most interesting stories to tell? Whether it’s a trip to a foreign country or a tale of survival, stories bring the storyteller to life.
Our stories make us unique.
You don’t need an eccentric sense of style or a contempt for pop culture to stand out. You only need to experience life and live to tell your story. Maybe your story will be similar to someone else’s, but it could never be completely identical because the only person who can live your life is you.
So go live it. 
Cherish it.
Remember it.
And then share the stories of your life with others because that’s what makes you unique.