In 1853, American Naval Commodore Perry showed up with a fleet of warships, canoned Edo (modern-day Tokyo), and demanded that Japan open its borders--which had been closed to foreigners for years. This caused a revolution within Japan--one side, the Tokugawa Shogunate, wanting to keep power and maintain society as it was, while the other side, the Imperial Revolutionists, wishing to modernize Japan and make it a world power.
From 1853 to 1868, a civil war called the Bakumatsu raged around Japan as these two sides battled for control. The Imperials eventually won, and in 1868, established the rule of Emperor Meiji, relocated the capitol of Japan from Kyoto to Tokyo, and began opening its borders to foreign powers like America, France, Germany, and the like. This began the Meiji Period in 1868.
If you want an entertaining, if not exactly historically correct look at the results of the Meiji Restoration, you can watch the anime Rurouni Kenshin or see the movie The Last Samurai, both which take place about ten years into the Meiji era, showing the results of the restoration.