The first line in the quote now in the question defines a function $f$ of variable $n$. The last line is about how fast (the output of) that function grows when $n$ grows.

Both statements $f(n) = Ω(n^3 \log n)$ and $f(n) = ω(n^3 \log n)$ tell that $f$ grows faster than the function $g$ defined by $g(n)=n^2\log n$. The second statement implies the first.

Anything more specific won't meet the "high level explanation" requirement in the question. But if we read a few lines _above_ the question's quote in the book, the definitions are given.