This function is all about
meaning in the completely personal sense. You must have meaning in your life, something important, something that you know that you were made for, and where you fit in completely. This is the only way you can settle down your Ni-Demons that keep creeping up on you every time you are in a state of "inaction". (Also, this is why Si as a life philosophy is unsatisfying, because it is not important to the intuitive experience of "finding your place in existence".)
Just like Ne will generally try to find the "meaning" of events and objects that are "out there", Ni will try to find the meaning of the things that are "inside" of yourself. And since it is based on intuition, it is very vague, and general, and tough to pin down, and mixed up with the unknowns of your own subconcious and human experience (something that we all share.) Therefore, your "meaning" that you try to find within yourself will be somewhat general, and vague, and difficult to pin down, and the information involved is heavily abstract (way more abstract then Ne) and will only come to you as hunches, and beliefs and such. But all these things are based off of your own subjective, introverted, experience. Thus, they will only be specific to you.
I can see how this can get confused with the Ti "understanding and logic", but the big difference is that Ni is a "perception" of things that come from inside you. You "learn" Ni from your intuition and subconcious. Ti is something that you "derive" by trying to be objective.
To sum it up:
Ni - meaning of your existence, finding a place to fit in, what you were made for