Spirituality has a different meaning to each of us, it seems. A standard definition would be: "A sense of meaning and purpose; a sense of self and of a relationship with 'that which is greater than self".
Currently, Religion and Mysticism seem to have the monopoly on Spirituality. Theistic religion often regards a 'relationship with god' or divine creator, as a spiritual relationship, while Mystics will often find a relationship to a 'supernatural' force or power. The bottom line is that, almost universally, spirituality has to do with a 'relationship' on one level or another. In most perspectives, it is associated with a person's 'place' or 'meaning' in life... whatever that may be.
As subjective as these things can be, we begin to recognize changes in these notions, for social progress tends to carve a path for understandings that stand the test of time. In the modern age, we have the ability to look far in our past and examine what our ancestors used to consider 'real', and then compare those ideas to what we understand today. Many "spiritual practices" which have existed in the past, no longer exist due the understandings that have come about in regard to natural phenomenon. As a base example, early religions often 'sacrificed' animals for certain purposes... this rarely happens today, as the relevance of such an act has proven pointless in its desired effect. Likewise, rarely do people perform 'raindances' in order to influence the weather... today we understand how weather patterns are created, and ritual practices have no provable effect.
Similarly, the idea of 'praying' to a god for a particular request, has also statistically proven to have little effect on an outcome, not to mention the evidence to support a personified creator doesn't exist in any scientific way...rather it is often derived from ancient historical literary speculation and tradition.
Establishment Religion, in many ways, seems to be rooted in a perceptual misunderstanding about life's processes. For instance, it presents a worldview which often puts the human on a different level than other elements of nature. This 'spiritual ego' has led to dramatic conflicts for generations, not only between human beings, but inadvertently between us and the environment itself.
However, as time has moved forward, Science has shown how human beings are subject to the exact same forces of nature as everything else. We have learned that we all share the same atomic substructure as trees, birds and all other forms of life. We have learned that we cannot live without nature's elements... we need clean air to breathe, food to eat, energy from the sun, etc. When we understand this Symbiotic relationship of life, we begin to see that as far as 'relationships' are concerned, our relationship to the planet is the most profound and important. The medium by which this is expressed, is Science, for the Scientific Method has allowed us insight into these natural process, so we can better understand how we 'fit' into this life system as a whole.
This could be called a 'spiritual' awakening.
This realization, which has been proven by science, is that humans are no different from any other form of nature, while our integrity is only as good as the integrity of our environment, to which we are a part. This understanding presents an entirely different 'spiritual' worldview, for it forces the idea of interdependence and connection, at its core.
The interconnection of the whole of life is undeniable in the most basic sense, and it is this perpetual 'relationship' of total interconnectivity that is not fully realized by society overall. Thus, our modes of conduct and perception are largely out of line with nature itself... and hence destructive.
Nature itself is our teacher, and our social institutions and philosophies should be derived from this foundational and, invariably, 'spiritual' understanding.
The faster this spiritual awakening spreads, the more sane, peaceful and productive society will become.