"Core essence" is who you are, your core nature and important qualities, such as spirituality, personality, your demeanor, your character, and morals. The physical body, handicapped or not, is usually not considered part of the definition of "core essence." When patients, elderly, or handicapped have animals around, they are more vibrant, and feel alive when not being judged by others or themselves, for the things they can't do while they are sick, or maybe never again. Since animals don't judge there is the sense of freedom of emotions. No judgment. The animals like them for who they "are," not who or what they cannot do or be.
Hope this helps!