Rain is treated here as a visitor you actually want, someone you open the door to and talk with like an old friend. The speaker asks a series of questions, and the poem reads as an invitation to the reader: do you, too, let the rain into your home and into your soul?
The rain becomes a kind of confidant. The speaker imagines packing up deep, dark secrets in a briefcase and handing it over to be carried away. Tears might go in as well, or they might wait until the rain has left, when they can soak you instead. Either way, the storm gives permission to let go of what you've been holding on to.
The mood is quiet, tender and a little wistful. The ending shifts to relief, with the clear sky making you feel like a newborn. The trailing dots suggest that this freshness will last for a while, but not forever.