Dark secrets and embarrassing moments people would rather not speak about again. These can range from smaller things like adultery to bigger like rape. Whatever the 'body' is, it is a dark memory the person would rather people never found out about. This phrase tends to be used with rich middle eastern people who are obsessed with cars.
The act of acquiring new sexual partners in a repeated fashion. Any sexual partner you have previously had intercourse with is no longer eligible to be considered a "new body".
Paul: "Yo Jimmy, you catch any new bodies this weekend?"
Jimmy: "I fucked one beat chick but.... THAT'S A NEW BODY!"
Paul: "Hell yeah brother."