In the Noon crash course, a core is defined as a cell whose tail is data (possibly containing other cores) and whose head is code containing one or more formulas. The head of a core is call the battery and the tail of a core is called the payload.
A formula in the battery of a core is called an arm of the core.
An arm is evaluated by applying it to the core it's part of, sort of like a method on a Python class taking only self.