I heard it was a way to show how sorry you were for fucking something up or dishonouring your family. You'd present your severed pinky to your boss as an appology. Apparently it's not done much anymore. I've played all the Yakuza games so I'm basically an expert.
I recently watched a great documentary about the Yakuza (on Arte) and apparently that ritual is increasingly considered old-fashioned among the Yakuza, or what's left of them.