Vessel is a hard story to explain. It was actually a vivid dream I had, which is why I guess it's so confusing. I can't really explain the whole opening, so I'll give just the main plot. A younger man named Rei Yosuke, is a top level officer of a phychic organization called the V.C.A. (Vessel Care and Asisstance) that is in charge of facilitating Vessel Transfers; a ceremonial soul swapping. He is sent to aid an odd case that has never before been encountered when a man's spirit has entered the body of a woman named Ino Housui. The case isn't rare becouse of the sex swap. It's rare because the two were complete strangers; there was no ceremony whatsoever. Rei's job is how the two souls switched, if in fact that is what happened.
I know that doesn't explain much, but trust me it's pretty damn complicated.