What is it?
The easiest relation to the term Living Force would be "Background Energy" yet that is a very poor definition. While The Living Force does not actively do anything, it is the source of energy that provides life, and is also bolstered by the existence of life. This is a situation where no matter how much you take out there is always more water in the lake. As a result each person contributes to The Living Force and increases it, this is why to many who study the Force that life is sacred. Likewise however this aspect of the Force is static, and can be affected by the status of the Personal Force of people within it.
How does it work?
The Living Force is the source of all energy, and as such must be everywhere all at once, and in infinite potential. However, this also means it may be left with any imprint on it. On the one hand it is an unlimited power supply, yet also the ultimate recording tool. Whatever frequency of energy is near the Living Force it will feed more into that Frequency, helping to perpetuate the fact that energy is never destroyed, and likewise will in turn take on properties of that energy near it. This goes for locations, people, emotional states, everything.
How does it affect me?
The Living Force provides you with life, a way of sensing others around you at a distance because of its limitless potential, and a way to know where you are at instinctively as it presents to you all that has happened within it in its location. Likewise it presents an infinite resource of energy to a Jedi, as it is where their power flows from into and through their personal Force.
How does it affect others around me?
The Living Force affects others around you the same way it does you, yet also allows them to see all that you have affected it and within it. As a result it is a way for others to know who you really are, know what you represent, and know what to think of you without them imposing on your Personal Force. Likewise any affects you use your personal Force for it spreads through the Living Force in at least a small way.
How does a Jedi relate to this aspect of the Force?
This is where a Jedi makes use of their senses the most. Through the Living Force a Jedi may sense anything, anywhere, at anytime, in all times and all realities that have existed, may exist, or could possibly exist. Infinite is a rather large term and it applies well to the Living Force. This is also where a Jedi draws their strength from, as when the Living Force is pulled through the Filter of the Personal Force the Personal Force expands.
This aspect is the most important because it provides knowledge of what has come, may come, and is happening, and provides an inexhaustible supply of power to those who may tap into it.