A couple of partially incomplete answers so far, so here ya go.
Modern RVs (1970s and newer) have at least two separate waste tanks. One (or more) for "gray water" which is connected to the sink and shower drains. And one for "black water" which is connected to the shitter only. When any of the tanks fill up from normal use, they need to be drained or "dumped." If you're staying at an RV park that has full hookups, then each RV pad has a hole in the ground, with an underground pipe that is connected to the RV park's septic tank, or potentially directly to a municipal sewer system. You leave your RV connected to that hole via a flexible 3" ribbed hose, aka as a "stinky slinky," and the when the shitter's full, you open a valve and the tank drains into the hole. If you're not staying at a place with full hookups, like most state parks in Texas, then there is a separate "dump station" on the way out. So when you're leaving your campsite, you should stop at the dump station, connect your stinky slinky from the RV tank dump outlet, to the campground's dump station's hole, and let your tanks drain before you leave.
If you're dry camping or boondocking off the grid at a place with no dump station, then there are other options. Many truck stops have a dump station that might either be free, or you can use for a small fee.
Since there was no dump station available in Clark Griswold's driveway, Cousin Eddie was just dumping that sewer hose directly into the gutter or sewer outlet in front of Clark's house. As you might imagine, this is illegal and not a great idea.