Buddha-nature/tathagatagarbha is not a singular notion. It is something has varying explanations, depending upon when and where the doctrine is looked at. But, in its most basic form buddha-nature is expressing our potential to awakening because we are empty of any unchanging, self existence thingie-hood:
Samyutta Nikaya III 144: "Bhikkhus monks, the Buddha said, holding
a fleck of cowdung on his palm], if even if that much of permanent,
everlasting, eternal individual selfhood/metaphysical being [attabhava],
not inseparable from the idea of change, could be found, then this living
the holy life could not be taught by me."
The nest expresion of buddha-nature I have come across in the Mahayana is from Dogen: "Impermenance is buddha-nature
As a concept, the only problem I have with the idea of buddha-nute is that it tends, in common usage, to end up sounding like a self substitute: "I have buddha-nature."
And for your edification, a full throttle explanation from the Tibetan Gelugs:
-- The tathagatagarbha [buddha-nature] is not just any emptiness,
however. Rather it is specifically emptiness of inherent existence when
applied to a sentient being's mind, his (her) mental continuum. ... When
the mind is defiled in the unenlightened state this emptiness is called
tathagatagarbha. When the mind has become pure through following the
path and attaining Buddhahood so emptiness is referred to in the dGe
lugs tradition as the Buddha's Essence Body (_svabhavikakaya_). The
Buddha's pure mind in that state is his Gnosis or Wisdom Body
(_jnanakaya_), while the two taken together, the Buddha's mind as a
flow empty of inherent existence, is what the tradition calls the
_dharmakaya._ ... This also means that the tathagatagarbha itself is
strictly the fundamental cause of Buddhahood, and is no way identical
with the result, _dharmakaya_ or Essence Body as the case may be,
except in the sense that both defiled mind and Buddha's mind are empty
of inherent existence. ...which is to say that even the _dharmakaya_,
and, of course, emptiness itself, are all empty of inherent existence.
They are not 'truly established', there is no Absolute in the sense of an
ultimate really existing entity. --- Paul Williams MAHAYANA
BUDDHISM, pub by Routledge. Pg 106-7.
And this is why I'll take Dogen's more practical explanation.
This being is bound to samsara, kamma is his means for going beyond. -- SN I, 38.
There is freedom from birth, freedom from becoming, freedom from making, freedom from conditioning. If there were not this freedom from birth, freedom from becoming, freedom from making, freedom from conditioning, then escape from that which is birth, becoming, making, conditioning, would not be known here. -- Ud 80
Ar scáth a chéile a mhaireas na daoine.
People live in one another’s shelter.
dheamhan a fhios agam
Damned if I know.