Spiritual understanding relates to considering things as abstract concepts. It brings together what is similar in many physical instances, enabling universal generalisation and prediction about observation. The explanatory power of language is spiritual in nature, with words a rendering of knowledge by the human spirit. This is how I understand it, with spiritual effectively a synonym for conceptual. This is the sense in which we say science is one of the great achievements of the human spirit.
The merely physical is apprehended by sense perception, while the spiritual is comprehended by reason.
Spirituality presents great scope for false consciousness. False spiritual faith (eg the dogma of the Virgin Birth) claims access to a higher miraculous comprehension that is not available to ordinary perception, but with this claim it separates itself from reality.
Your observation about animals 'living their bodies' relates to our previous conversation about instinct, and how reason separates humans from instinct. The irony is that it is only through conscious reasoning (ie spirituality) that we know how many haemoglobin molecules there are.