It is somewhat hard to argue right now that Japan is growing in power, but it is easy to argue that China is doing so. China is growing in power largely because it a huge country in the midst of an economic boom. Furthermore, its boom is coming just as the countries that are already rich are in something of a slump.
China has been growing economically because it is a country that has had relatively low labor costs, a stable government, and an educated populace. This has made China very attractive for Western (and Japanese) companies wanting good productivity at lower wages. Because China has been growing economically (particularly as rich countries stagnate) it has also been gaining military power. It is nowhere near to the strength of the US military, but it has, for example, gotten an aircraft carrier as a way of projecting its power further than it ever has before.
Because of its growing economic and military power, China has gotten more diplomatic power as well. It has used its economic power, for example, to gain more influence in African countries that need investment. They prefer Chinese investors to Western ones because the Chinese do not try to encourage the rulers of the country to pursue human rights or anything like that.