Function of UCC2813-1 in flyback converter
RF and RC, COMP and REF, CS and COMP and how they effect overall
  function of IC.



RF doesn't exist as a pin so maybe you mean REF (also see below) and the use of the oscillator resistor to REF (see RC pin) ensures the RC oscillator frequency is kept at a fairly constant frequency irrespective of power supply changes or variations.
RC is for placing a resistor and capacitor for creating an oscillator - read the data sheet page 6 for precise detail
COMP is the comparator output and again the data sheet is quite useful - the symbol is a triangle with an invert circle on one of the inputs. This is equivalent to an op-amp type symbol with a "+" on the non-inverting input and a "-" on the inverting input.
REF - REF/2 (half the voltage of REF) is used as the comparator input for comparing the feedback voltage with. When normally running, the fed-back voltage will nominally be the same level as REF/2


To go into much more detail is probably going beyond the bounds of EE's question and answer format. This circuit might also explain things a little better: -


(source: datasheetdir.com)  

It's a very similar device to the one you have specified.