It is difficult - I would say impossible - satisfactorily to define The Spiritual, except as a 'diagnosis of exclusion'.
In other words, the spiritual is that which is not material;
or, the spiritual is the immaterial.
This was, indeed, the definition of spiritual suggested by Owen Barfield (after are careful examination of the history of language); and while it is correct, it is not fully satisfactory - because the definition of 'the material' has been fluid through time, in a way that shows the reality of the spiritual as being (more or less)
that which contemporary modern culture regards as unreal.
For example - mathematics was, at one time, regarded as spiritual, mystical - and Mathematicians were if not theists (believers in a personal God) then at least deists (believers in an impersonal creating-deity). This was the case for many - perhaps all - of the great early scientists such as Newton. However, the development of modernity included mathematics within science, and excluded all non-scientific uses and functions of mathematics to the realm of pseudo-science or 'superstition'.
A more recent example is quantum theory. As Barfield remarks, this branch of physics has many spooky and immaterial aspects which would normally have made it a spiritual subject; however, it has been included in mainstream science and any consideration of the general implications of quantum theory for human life have been ruled-out and (as with mathematics) consigned to the realm of pseudo-science and ignorant superstition.
An example of personal relevance has been Rudolf Steiner's remarkable 1918 prophecy about which I have written recently. Steiner (I believe correctly) regards the recognition of 'the spiritual' as primary and essential task of our era - in Barfield's terms this corresponds to the next step in the evolution of consciousness to Final Participation.
However, putting so much weight upon the concept of The Spiritual is problematic when the definition is negative - and the same problem arises in the 'mission' of this Albion Awakening blog to promote a new and 'spiritual' kind of Christianity.
I think the correct formulation is that Western Man must become more spiritual by reunifying the material and immaterial - and this unification happens quite naturally and spontaneously as a consequence of the evolution of consciousness to Final Participation by means of what Steiner terms 'pure' thinking and I have termed 'primary' thinking: that is, the conscious, purposive, free-agent thinking of the divine-self in Man.
Primary thinking is also a kind of intuition - and in intuitive thinking there is no division between material and immaterial; because the thinking is (simply) assumed to be in the universal realm of reality, which contains all kinds of things; some that we would call material and others that we would not.
Therefore, a return to The Spiritual for modern Man actually involves the abolition of the category of Spiritual - we would (rightly) cease to be concerned with the categories of material and spiritual.
And that change and unification is precisely the necessary evolution which Steiner (in 1918) argued was our divine destiny.