Monster Island is an island within the Toho Universe that Godzilla along with other Kaiju are said to inhabit, depending on the film. The Island took many forms over the course of the series, sometimes being inhabited solely by the monsters and at other points being controlled to some extent by the Japanese or World Government. Monster Island or Monster Island like locales were commonly used in the more child friendly Godzilla films of the late 60's and early 70's, though fell out of favor by Godzilla vs. the Cosmic Monster.
A Monster Island like locale would show up again in two Heisei films, Godzilla vs. King Ghidorah and Godzilla vs. Space Godzilla though the convention has not reappeared since then.
During the late 60's and early 70's, Monster Island was frequently used as a way to get Godzilla and any other monsters involved, into the movie without a lot of back story, especially in Godzilla vs. Gigan and Godzilla vs. Megalon. However, by the time that Terror of MechaGodzilla rolled around, Godzilla simply appeared on cue. It was also a way for the producers to fill up time by including stock footage of the other monsters.