I'd need a little more context to be sure, but "into the blue" usually means into the unknown or into open and uncertain spaces. So in this context it probably means the person jumped into an unknown or uncertain situation.

"The Blue" is a nickname given to the ocean, mainly referring to the deepest and furthest reaches where nothing can be seen below the surface as well as not being able to see land in any direction. In whichever direction you look you don't really know what is there and that's where we get the phrase "into the blue" meaning going into a situation that you know nothing (or very little) about There is also a related used of the term in the phrase "out of the blue" which means to arrive unexpectedly as though appearing from nowhere.