On three legs of a CFO stool...

To give structure to a CFO role, consider it to be a three legged stool.

1) Accounting/Auditing/Control:  The nuts and bolts of finance.  This area covers accounting, governance, payroll - activities that are essential to any business.  Usually when a business starts, this is the first area to get setup. 

2) Financial Operations:  This pertains to business finance, finance support, operations, planning, FP&A.

3) Investor Relations:  This is the art part of the CFO role.  It involves managing investor expectations, and working with capital markets.  For simplicity, Treasury activities can be combined under this leg.