What is the story, what is going on, what is happening, what is the background.
What is the skinny on this White water thing?
This is a shortened version of the skinny naked truth which comes from WW2. Skinny in this case meaning resembling skin and being redundant with naked. This phrase literally is asking for the naked, unobscured truth.
Alternative: Skinny is defined as inside information. Hence what's the skinny literally asks what is the inside information. This definition may derive from the skinny naked truth.