Think of it as you sticking your finger in the end of a garden hose.
What happens when you stick it way down in the end of the hose?
The volume of flow decreases.
What happens when you pull your finger out?
The volume of flow increases.
Raising the clip (away from the pointy end) lets the needle sit lower in the slide, thusly lower in the needle jet, reducing the volume of flow. (Leaner)
Lowering the clip position (towards the pointy end) lets the needle sit higher in the slide, thusly higher in the needle jet, increasing the volume of flow. (Richer)