I am not the person you asked this question of, but for me personally (which could be completely out of line with how it is for others) I think of it mostly in terms of attachment and trust. Like... having a human being who holds you in positive regard, faith and love. Someone who has your back no matter what. Someone who is there to guide or support you and catch you when you fall. That one person who you can trust with your most vulnerable self.
Like many other people I never had that from anyone before. I feel getting that from someone was critical in getting me to the point where I could accept my Self (selves).

I call what happened in our relationship with that T 'reparenting'. Because she taught me what the parents should have taught us - that we are a valid and acceptable member of the human race. We did not know that until we'd had many years of therapy with her.
We haven't been in therapy with her for many, many years now, but when we *truly* need support (a.k.a. when the s*** of life hits the fan) we still turn to her.