Zentai are opaque, skin-tight suits that cover the entirety of the face and body. The word is a Japanese contraction of zenshin taitsu, which means "full-body tights". Think of them as the ultimate in adult onesies. Because they're typically made from Lycra or similar spandex-nylon blends, it is possible to breathe, see and even drink through the garment. Zentai are donned by means of a long zipper at the back.
Zentai hobbyists typically value them as fetish outfits. They can be worn in private (whether alone or with 'friends') or used for exhibitionist purposes, exploiting the anonymizing properties of the full facial hood. That said, it isn't always a sex thing. You'll see zentai in Japan on shows like Power Rangers, but the Western Hemisphere has also occasionally taken advantage of the suit's unsettling and somewhat supernatural appearance. The Green Man on It's Always Sunny in Philadelphia and The Greendale Human Being on Community are examples that spring to mind, not to mention the much more familiar Spider-Man.
There's even a culture jamming group called The Zentai Project whose members go on urban walkabouts, amusing – and weirding out – the general public.
Obligatory pictures here and here.