Several of Nature’s People I know and they know me
So, now we’re back to the grown up speaker talking to his audience.
He's got friends, don't you know. Specifically, "Nature’s People" are some folks he knows.
He also feels compelled to tell us that they know him, too. Why? Wouldn't it be enough to say, "Those Nature People? Oh yeah, I know them"? It seems that it's not. He wants us to know that they know him, too.
Maybe this back and forth has something to do with who the speaker knows. "Nature People"? Does he mean hippies?
Probably not, since Dickinson wrote this long before the Grateful Dead showed up. More likely, this refers to the snake and the rest of the critters that live out in the natural world. We might call them animals.
Our speaker doesn't, though. Again, the line between people and animals is blurred. Not only are these animals "People," to the speaker, they're also capable of "knowing" him. This relationship is a two-way street, and the animals are able to "know" the speaker as we might know a person. Once again, we're hit with a helping heaping of personification.
I feel for them a transport Of Cordiality
Woah. Some confusing terminology is going on here. Let's take it bit by bit.
"[T]ransport" is a weird word that would usually be used for the religious and spiritual highs of saints and holy people, but it also means to carry something from one place to another.
“Cordiality” is the pleasure that you feel either hosting a guest or being a guest.
So, in other words, the speaker feels either the ecstasy or the transfer (or both!) of hospitable feelings toward "Nature's People."
Put simply, he's a fan of animals. The way this idea is presented, though, shows us that such feelings are not that straightforward. He feels some deeper connection to them.