Mathematician, Pierre-Simon LaPlace was once asked by the emperor of France where God was to feature in LaPlace's mathematical system. LaPlace replied, "I have no need of that hypothesis."
The idea behind the quip is that if you can find a good explanations for something without God, then you don't need him. And if you don't need him, then this is good reason to suppose that he's not there.
The kind of God supposed in such thought is the "God-of-the-gaps" kind of God, a God who is necessary only in so far that he explains some feature of the world - existence, the movement of the planets, the habits of our species, or the events of history. No Gaps, No God.
The trouble is: there is no such God.
If God exists, he would not be such a being as to only involve himself where he was needed. Instead, God would be involved in everything - responsible for the workings of all the laws of nature not merely for the ones that need a divine hand.
Second, belief in God is not dependent on gaps in explanation. Theists don't (or shouldn't) believe in God purely because they can't come up with a better explanation for the existence of the world. Indeed, the Christian believes that the reason they have beliefs about God is that God has revealed himself to us - through nature and through scripture.
A scientific explanation is an attempt to explain some given phenomenon. When we come to a good one we settle on it. But God is not reducible to a scientific explanation.
This is not to say that saying God explains the world is wrong - God is plausibly the best explanation for all those things I mentioned - existence, the movement of planets, the habits of our species, and the events of history. He is even the best explanation for the fact that humans are able to think about such things in the first place. Indeed, another way of saying that there is no God-of-the-gaps is saying that there are in reality no gaps.