RC style stands for Row/Column style. In this style, rather than letters and numbers, addresses are given only in numbers. Numbers in square brackets give relative position, while regular numbers give absolute position.
So, let's take a look at the first formula. Everything is given in reference to G4.
=SUMIF(C3,RC[-1],C2)
The "C3" at the beginning is not the cell C3, but rather column 3. Since there's no R component, this is a reference to the entire column. Since there's no square brackets, C3 is equivalent to writing "$C:$C"
Next, RC[-1] is the 2nd argument. There is an R component, but no number given. This means that the cell will be in same row as our reference point, G4. So, we'll be in row 4. The column given is relative reference, 1 column to the left (aka, -1) of G4, so the address RC[-1] is referring to F4.
Finally, "C2", similar to the first argument, is an absolute reference to 2nd column, aka, $B:$B.
In conclusion, this:
=SUMIF(C3,RC[-1],C2)
is the RC equivalent of:
=SUMIF($C:$C,F4,$B:$B)
The 2nd formula in H4 will evaluate to:
=COUNTIF($C:$C,F4)