Do you remember the 90's? The Simpsons was still good, Y2K was considered a serious issue, and our presidents stopped being the "greatest people ever". It was a sort-of simpler time, and then South Park happened.
Cartman Gets an Anal Probe introduced Stan and Kyle, who are as normal as you can get in this town. We weren't shown a cartoon that was showing us some nice innocent kids like we were used to, they were showing us Peanuts on drugs. These kids are foul-mouthed, dirty, mean, and, most-of-all, hilarious. However, it's still clear that these two kids are the normal ones compared to Kenny and..well, I'll let the next paragraph explain my favorite character.
Even in the first episode, Eric Cartman stands out as the crowning comedic masterpiece of the show. He's absolutley everything you'd hate about a real-life kid, but, somehow, they make him the funniest character you've ever seen. He really showcases the style of comedy the show is going for; the "we don't care who we offend" type of deal.
Lots of Cartman's lines in this episode rightfully become classics. His famous "Screw you guys, I'm going home" line actually first appeared in the pilot episode. Counting off the funny moments, there's Eric fighting with Mr. Kitty, Mr. Hat yelling at Kyle, Chef's first song, Stan puking on Wendy, etc.
The animation is different here, but what do you expect if it's made out of construction paper? It doesn't have the perfect comedic timing that the following episodes do. Despite that, it still works by driving on one thing and one thing only: jokes. You have visitors, anal probes, and Ike all in one little episode. What more could you want from a pilot?