Real simple example using a song I love would be Porcupine Tree's "Collapse The Light Into Earth." It's a good example because it's 5 chords on loop for the whole song, but everything else really changes the way we experience those chords, and that's what counterpoint is all about.

It's first about music as "voices" and kinda separating out the instruments to just what notes they're bringing to the table. Then it's about stacking those notes together and taking a look at what "chord" exists at any given moment.

Then, if we get nerdy, we start talking about how the individual voice shifts and choices in how to voice lead to specific chords support the... feelings it makes us feel.

So, Collapse the light into earth is 5 chords on loop. They're all triads. Nothing fancy. Bm, Cmaj, Gmaj, Dsus4, Dmaj.

Since I don't have sheet music or a pen and paper, I'll note that, for example, the chorus, Steven Wilson sings "Co - lapse, the light, into earth" The "Co" is a B and lasts the whole measure with the Bm, Nothing strange here. Good support of the well established idea. But then bar 2 of the chorus, "-Lapse" is a D. Over our Cmaj. Making it kind of a Cmaj9, but it's kinda wedged in there with the chord instead of floating over it, so it's kinda spicy. It's no regular C major anymore. And in this way, the Chorus and the Intro are distinct, despite so much remaining the same. Our analyzing the Cmaj as a Cmaj9 is a piece of contrapuntal analysis. (if I wanted to continue to be nerdy, I'd not that this D is the same D that the next three chords all hinge around. That D is at the center of the G, the Dsus4, and the D, the way it's voice led. So this choice to bring that D over the C major, the only bar where there is no D otherwise present, feels intentional so as to create a lot of strength around that note. To really keep the song centered around that droned D).

If you listen carefully, you'll notice the vocal melody does this not just in the chorus, but all over the song. And... not just the vocal melody, but the bass... and the synths that come in the later half... The song is a very, very rich example of counterpoint, mostly because you can see how bastardized the original 5 chords look at any point in the middle, despite them being really actually at their core not very far off. Just, embellished. It's fun.