What did Cartman mean here by Rainbows?

This is a common theme in the early seasons of the show- the overriding theme is that Cartman is constantly picking up these bizarre "facts" from his mom, who is of course on the cover of Crack Whore magazine. In another early season episode, "Ike's Wee Wee"(season 2), Kenny answers Chef's question of what is more sacred to a man than anything (referring to the penis) in his muffled tone, and Cartman responds "You're not supposed to call it that, Kenny. You're supposed to call it a Fireman, that's the proper term, or else you get a spanking."

I think the general idea is these little snippets provide a window into how bizarre Cartman's home life is, and whatever he thought Rainbows were probably fit into some odd thing his mom said. Great line, one of my favorite episodes!

According to several fan forums, like this one, Cartman's rant has its origins in something Matt and Trey encountered:

The Rainbow sequence with Cartman does not refer to anything. Believe it or not the rainbow thing is a totally obscure reference to nothing at all. One day Matt and Trey were eating in a restaurant and they heard some girl say that she hated rainbows and that is where they got the idea. It's as simple as that.

This would indicate that it is included here simply as some absurd joke, and that looking for an explanation of Cartman's words might be futile.

The script that you posted touches on your exact question:

Stan: What were you talking about?

Stan is asking the exact same question as you.

Cartman: Huh? Oh, nothing, forget it.

And that's the answer that Stan (and by extension you) gets. Cartman is avoiding the topic, because he doesn't want to talk about it.

The humor derives from Cartman's willful omission of any further explanation.

There are several possibilities as to why he feels that way. Most likely, Cartman feels embarassed about what he was talking about. Keep in mind that he's talking about creatures that crawl up his ass.
When he thought that the boys were already talking about these creatures, he felt comfortable talking about it. But now that he realizes that no one was talking about these ass-crawlers, Cartman doesn't want to publically embarass himself any further, and instead tries to avoid the topic.

Edit

The continuation of the above script:

Stan: What were you talking about?
Cartman: Huh? Oh, nothing, forget it.
Kyle: No. What marches in, crawls up your leg…
Cartman: Nothing.
Kyle: …and starts biting the inside of your ass?
Cartman: Nothing.

And that's the last we hear of it. Cartman never specifies what he was talking about.