What does it mean that Hashem is One and that there is nothing in the world except for Him? What does the Ba'al Ha'Tanya mean (chapter 20) that Hashem Echad means that He is alone in the world and that everything else has no existence? In what sense do I have no existence?
There is a base reality which everything conforms to and from which everything springs. This reality is why the law of gravity is the way it is, and every other law of nature. It is the force behind everything.
The theoretical alternatives to this concept are (1) that no force exists behind any law (and the laws of nature are not really laws, but random patterns with no necessary force to them); or (2) that multiple such underlying realities exist. The notion of Hashem echad rejects both of these alternatives; why is a separate discussion.
Thus, Hashem echad is the concept that you and I exist only as building blocks upon that base reality. Our existence has meaning only in relation to that reality. If we isolate that reality -- we can't, but if we could imagine it not existing -- we would necessarily have to imagine ourselves not existing either, because everything real is only real insofar as it relates to reality. If something has no relation to reality there is no sense in which it can be called real.
In this sense, Hashem's existence is more basic than ours, more real. He is reality itself - what will be, what is, and what was - while our existence is just relative to his.
See also Derech Hashem, Ch. 1.