Tokusatsu is a Japanese term that means "special filming". As a genre it refers to pretty much any live-action production that makes extensive use of special effects. In the literal sense, anything from Wonder Woman to Doctor Who could be considered tokusatsu but, much like "anime", it is used colloquially in English to refer specifically to shows and movies of Japanese origin or adapted from them. Popular examples include kaiju movies like Godzilla, superhero shows like Ultraman and Power Rangers, and inter-galactic space operas such as Gorath and Warning from Space (known for influencing 2001: A Space Odyssey).
The genre has its roots in early Japanese theater, which made extensive use of special effects. Another influence was Japan's kamishibai medium, which introduced fantastical sci-fi elements such as mechs and flying caped superheroes like Golden Bat and Prince of Gamma (popular in early 1930's Japan, years before Superman and Batman were created in America).
The first video game to draw influence from Japanese tokosatsu movies was the American-developed Spacewar, the game responsible for launching the video game industry.
Being a popular and influential genre in Japan, many Japanese developers apply inspiration from various Tokusatsu works into their games. Some popular examples include Viewtiful Joe and The Wonderful 101.