What is it?
This is the aspect of The Force that gives knowledge of Right and Wrong actions, connects The Living and The Personal Force, and gives purpose to the substance of reality.
How does it work?
The Force, as in all things, exists to perpetuate, to become more than it is. As a result this aspect of the Force reigns over this region of conceptualization. To that end this aspect not only guides, but connects all things together in a symbiosis. That is why life can not exist without The Force. The Unifying Force also thereby gives a common purpose to all living things, to do, strive, and become more than what they are, because in doing so it does likewise.
How does it affect me?
This is the aspect of the Force that not only allows you to know a right or wrong action instinctively, but allows you to grasp knowledge of these concepts. Likewise, this aspect of the Force connects you to all other beings in the Universe and gives you access to their concepts of reality. More importantly in linking you to all other things it makes it even more important that you continue to better yourself, for the lesser you are, the lesser all things are on some small scale. This is likewise the aspect of the Force that causes synchronistic events, miraculous coincidences, and nick of time results. It is through this aspect of the Force that all the possibilities become possible.
How does it affect others around me?
By linking all things to all things it gives a unity of purpose, and a sympathy of experience buried within all living things, and perhaps all of reality, in this it allows the lesser knowledge animals such as the dog to work along with the human, and the human to work with other humans for they each have a common bond to each other in ways they are not aware of.
How does a Jedi relate to this aspect of the Force?
This is the part of the Force that a Jedi trusts in, gains true wisdom from, and taps into for enlightenment. In essence one could easily say that at a point a Jedi finds the ONLY force is the Unifying Force, yet not all reach that point. Even without giving ones self completely to the unifying aspects a Jedi still draws their sense of purpose from this aspect of The Force.
This aspect is the most important because without this aspect no other aspects of The Force could be linked together. There would be no purpose in existence, and there would be no reason to perpetuate "good will" other than that of enlightened self interest. This aspect is so important not because of what it does, but because of the breakdown of cooperative reality that it prevents.