A declaration that social customs and unwritten rules are about to be ignored.
In other words, there is no law in the jungle. The biggest most vicious tiger gets to be the alpha male, eat all the meat, and have the most sex. So, this means declaring jungle law is simply declaring anarchy and doing what you want. It's an excuse to be an asshole.
Claire: "What the hell are you doing? I called shotgun."
John: "Well, I'm declaring jungle law and taking it. Suck it."