Why is it good to split a CTR-mode counter into nonce and counter?
Suppose you do CTR mode as:


  $E(k,nonce+1) \oplus m_1$, $E(k,nonce+2) \oplus m_2$, $E(k,nonce+3) \oplus m_3$, etc.


The wikipedia page is talking about a non-random nonce, with a specific example of a packet counter. So suppose $nonce$ is a packet counter and in each packet you encrypt several blocks. You might end up with the following:

In packet #$p$:


  $E(k,p+1) \oplus m_1$, $E(k,p+2) \oplus m_2$, $E(k,p+3) \oplus m_3$, etc.


In packet # $p+1$:


  $E(k,(p+1)+1) \oplus m'_1$, $E(k,(p+1)+2) \oplus m'_2$, $E(k,(p+2)+1) \oplus m'_3$, etc.


The nonces are unique, but CPA security is broken. You have used $E(k,p+2)$ as a mask twice, and are leaking the value of $m_2 \oplus m'_1$.