For me, with L anyway (not the first 2 t's I tried) it's a lot what Lost said above - she listens without judgement and accepts me for who I am. Having her sitting there talking with me and accepting every part of me even the parts I hate - helped me to gradually start accepting all of me as well. She's been kinda like a guide holding a lantern for me walking beside me on this journey to light the way. I hated myself for so much of my life. And talking with her, learning to first accept myself, who I am, and then finally actually finding grace and love for myself - I feel like therapy this time around has been instrumental in getting me there. I've grown in a lot of ways over the years. I'm still going because there's always more to learn about myself, always more self-growth to find, and it really has become something almost like a spiritual practice, this inner work. There's just something about the connection that I feel with her. Like, she really sees me. I don't feel genuinely seen really anywhere else.
Also what Lost said - I struggle too with when L says something that sounds like "what i want to hear" or like she quoted it out of a textbook. I didn't used to call her out on that, but I sure do now. Most of the time she sounds authentic and from the heart and that's what I respond to. I don't want to hear something that sounds unnatural and textbook-y.
She watches for patterns in what I talk about - I'm not good at seeing those in myself (I guess a lot of people aren't) so it's very helpful when she points them out to me.
Ok I need to stop now. I don't know if I answered your question or not, stopdog.
eta: what WFS said: "She heard my trees and was able to tell me about the forest." so eloquent and true for me also.
I just thought of another thing. She asks really good questions. And when I actually take the time to sit down with said questions between sessions and work on answering them, good stuff results.