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.
In sum; mathematics and quantum theory are now regarded as de facto material...
Continued at Albion Awakening