There is not really one answer to this Dan, but there was an interesting thread on it a while back in the spirituality forum. This varies so much from person to person but also with a lot of the same themes. http://forums.psychcentral.com/showthread.php?t=257569

I also am an atheist but my spirituality , ah hard to describe so I'll just try my best.

For me it is the energy I carry, that energy is also found in other things including plants etc. Quantum Physics would say that when they break down molecules into subatomic particles which have subatomic particles.. gets deep. They find the same pure energy. Infinite intelligent energy, and that we are all way more interconnected than we can possibly be aware of. Now for me this is where science and spirituality come together.

I also like to look to Hinduism which is a conglomeration of distinct intellectual or philosophical points of view, rather than a rigid common set of beliefs. I have found a great wealth of valuable ideas within Hinduism and texts. I also look to Buddhism in the same way. I am neither Hindu nor Buddhist but I blend ideas and philosophies from both with science and then of course I have my own ideas that fit within this too. It is highly debatable if either of those are religions, and not in the way we know religion in the west. They also both recognize atheism. So that works for me.

Hard to define it but for me living without spirituality is kinda like half living, Or living within only one part.. the physical. But to me they are part of each other. I feel like for me to really live in fullness I need to be aware of the sum of the whole. I feel my life feels more fulfilling, content, peaceful, and enriched when I nurture both aspects of life. I think this is why yoga is so big for me, it is a blending of the physical with the spiritual where these lines separating the two disappear and that is when I feel the most connected. I actually get teary eyed think about that feeling, because it is overwhelmingly beautiful, bliss. It can be very powerful.

But that link I gave you provides sort of complete definitions and quite a few of them.

Spirituality compliments religion if you are religious, you do see people who are religious but maybe not spiritually connected. Then you have spirituality with no religion, that exists also. They really are not the same thing. Religion is an organized collection of belief systems, cultural systems, and world views that relate humanity to spirituality and, sometimes, to morality.By that definition, spirituality is only part of religion, spirituality can lack the organization, morality, world views etc...

Hope that helps a bit.