Nothing Is Random, Everything Is Connected

"That there are no random acts. That we are all connected. That you can no more separate one life from another than you can separate a breeze from the wind."

    This means that everything you do will affect someone or something else.  It's like a domino effect.  Like in "The Five People You Meet In Heaven", many things that Eddie does affects other people, even people he didn't know. Then things that complete strangers did affected him in ways that were completely unknown to him until the end.  I think this is also a warning to be careful what you do because it could result in consequences on other people or on you. This statement describes karma and how everything that you do will come back on to you.
    This also means that even tough you believe that you are loving a life independent from everyone else, you really are not because things others will do will affect you and things you do will affect others. It shows you the consequences of what you do, good or bad, in your life. I also believe that this statement is true because karma is something that actually happens and this sentence describes it perfectly. You must always be aware of what you do and how it affects others.