In a sense, there are two Sino-Japanese Wars, but the one more commonly called by that name is the conflict of 1894-1895 (The latter, from 1937 to 1945, is generally lumped in with World War II -- by Western historians, at least.)

In 1894, the Manchu or Qing Dynasty ruling China at the time sent troops into Korea, at the invitation of the rulers of Korea, to help repress a revolt taking place there. By an 1885 agreement between Japan and China, one country could not send troops into Korea without the other being allowed to do so also; this was intended to keep either of the two powers from taking over Korea. So Japan, which had also been seeking to annex Korea for a long time, took the opportunity to send troops out as well. Japan had not declared war when it sank a Chinese ship carrying troops, but when the Chinese declared war on Japan on August 1, the Japanese also officially declared war.

China was defeated in eight months both on land and in naval battles, with its military strength greatly decreased and the Japanese occupying Chinese land in the northeast. Forced to send an envoy to sue for peace, China had to agree to a treaty stating that they would pull out of Korea, cede some Chinese territory to Japan, allow additional ports to be opened to Japanese traders, and pay a large indemnity to Japan. This treaty was not only unpopular in China, but was seen as a threat by the European powers who wanted to increase their spheres of influence in the area. Russia, France, and Germany pressured Japan into abandoning the territory of the Liaodong peninsula (next to Korea and seen as the obvious base from which to take over the now-independent country) in return for a 50% increase in the money paid to Japan by China. This final version of the Treaty of Shimonoseki was signed in November 1895.

The war would have a great impact on the future of China; the ruling dynasty's failure started up a lot of discontent and reformist or revolutionary thinking. People such as Sun Yat-sen who would figure in future events started their first revolutionary organizations during this war. And the European countries' policies changed in the area; in general, they felt more able to make demands of the Chinese government now that its weakness was proven. Great Britain allied with traditionally-isolated Japan; Russia worked against Japan and tried to make ties with China, though its ultimate intention was to gain Asian territory for itself (leading to the Russo-Japanese War ten years later). And Japan would invade Chinese territory again in 1937 in what some historians call the Second Sino-Japanese War.

Sources:http://nias.ku.dk/Neighbours/Sodbiligpaper.htm
http://www.fortunecity.com/olympia/ince/698/rurik/sino02.html
http://www.britannica.com/bcom/eb/article/7/0,5716,69707+1,00.html