1 is the country code for the US and Canada. When calling the US from overseas, you need the 1.
And, in Japan, you used to use 001 to first get an outside line (if I remember correctly...this is going back a few decades).
Then, the Japanese phone industry was deregulated, and Japan all of a sudden had three phone companies instead of the one national monopoly. Each phone company had their own prefix to get an international line; 010, 001, and another one...can't remember it now.
Bloody hell, I feel old.
It was like this in the US, too. AT&T was the only phone company. They had a national monopoly before sometime in the late 70's, I think. It was crap, too. Phoning overseas was super expensive - so expensive that you would avoid it at all costs. A short phone call to Japan could end up costing $100+ dollars.