For some people, [spirituality] involves a variety of very personal things like self-realization, philosophical searching, etc. For many others, it is something like a very deep and strong emotional reaction to "wonders" of life — for example, gazing out at the universe on a clear night, seeing a newborn child, etc.
All of these and similar senses of "spirituality" are entirely compatible with atheism. There is nothing about atheism which prevents a person from have such experiences or quests. Indeed, for many atheists their atheism is a direct result of such philosophical searching and religious questioning — thus, one might argue that their atheism is an integral component of their "spirituality" and their ongoing search for meaning in life.
Tradition: Atheist spirituality