The prefix of nomial refers to the number of glyphs taking into account when determining kerning. Hence a binomial kerning table employs kerning pairs, while a polynomial kerning table considers kerning triplets, quadruplets, and so on.
While this choice of words is somewhat justified by the Greek origin of binomial and polynomial meaning consisting of two/multiple parts, I consider it a bad choice as those terms are already taken by mathematics and relevant to type design as such. Usually, the term contextual kerning is used instead of polynomial kerning.
To illustrate the difference, let’s consider the examples from the quote. I rendered them once using only kerning pairs (top) and then adjusted the spacing as I would like it to be (bottom). Bear in mind that the latter is only a quick illustrative sketch and not perfect:
As you can see, with pair kerning, things do not look good. For example, there is too much space in V. and R.V. This is likely to avoid overlaps in combinations like V.V. Triplet kerning takes into account which letter is following or preceding the dot and thus it can place the dot closer to the V if appropriate. Moreover, it can harmonise the spacing in all capital–dot–capital combinations.
Quadruplet kerning could do things like harmonising the space in R. M and V. M by acknowledging that the V is leaning into the word space while the R is leaning away from it. However, the actual realisation of this in a typesetting program is unlikely, as they usually do not use the space glyph of the font but handle spaces themselves.