For me, the connection is the following:

She is my therapist and also my confidant. I trust her. It was hard won trust and I didn't give it easily.

The relationship between us is part of the connection, which includes her consistency and her caring for me.

We've developed a light psychic bond. Meaning, I will be doing something random and think of her and it turns out she had written to me in response to one of my emails.

She is connected to all of my parts -- meaning that there are versions of myself that will feel a deeper connection to the therapist than others. But even the skeptical and business competent parts now respect her value in my life.

If a therapist used the term, I think they'd mean something like clicking. Like, do we click? Is there a harmony here? Is there something that remains when we are apart that we can pick up again when we are together? Is there a familiarity? Is there comfort or trust?

In the physical world, we have data connections and electricity connections. It means there is something, a wire or a protocol, that allows the two sides to communicate effectively. It's not a perfect analogy but also fits.