A body spirit is the spirit(s) or soul(s) born into a body. Sounds simple, right? Figuring out who(s), if anyone is the body spirit, can often be a lot more difficult than it would initially seem.
Also, some multiple systems believe that more than one spirit was born into the body, resulting in more than one body spirit. It can also be argued that, similar to how some one celled creatures replicate themselves in ways that leave no discernable parent organism, ALL splits derived from the body spirit, are each in their own right, body spirits.
For some systems, the body spirit gets more say in body decisions, for other systems, this idea is preposterous, since as far as anyone can tell, the body spirit had left a long time ago.
The significance, if any, of being the body spirit within the system is something each system should figure out on their own.