"The four categories of existence, non-existence, both existence and non-existence, and neither existence nor non-existence, are spiderwebs among spiderwebs which can never take hold of the enormous bird of reality"
Dependent origination is the teaching of the Buddha which essentially states, "if this exists, that exists; if this ceases to exist, that also ceases to exist." It is the fundamental idea that all things in our universe existence depends entirely on the existence of other factors. This concept is covered very well by Thich Nhat Hanh in the example below:
"If we look into this sheet of paper even more deeply, we can see the sunshine in it. If the sunshine is not there, the forest cannot grow. In fact nothing can grow. Even we cannot grow without sunshine. And so, we know that the sunshine is also in this sheet of paper. The paper and the sunshine inter-are. And if we continue to look we can see the logger who cut the tree and brought it to the mill to be transformed into paper. And we see the wheat. We know that the logger cannot exist without his daily bread, and therefore the wheat that became his bread is also in this sheet of paper. And the logger's father and mother are in it too. When we look in this way we see that without all of these things, this sheet of paper cannot exist."
-- Thich Nhat Hanh
If this example does not convince you, make a game out of it. Try to think of anything you may come across in our universe that can exist completely on its own. When we look into quantum physics we see similar explanations for the universe. Nothing really comes into existence or leaves existence; matter and energy simply change forms.