In Japanese, they're called "dakimakura" (抱き枕). In English, they're "hug pillows". In short, hugging them while you sleep can either given a greater sense of security or even help with back problems.
The insinuation, however, is that hug pillows are otaku girlfriends. This is even a joke in Japan, tinged with irony—and most certainly not always true. Many otaku have real partners! Many more don't dry hump their pillows. And many simply use them to get comfortable.
But, let's say you have a hug pillowcase that you love and you think that something's missing. For you, there's Kuu-Pillow. It's an "a dakimakura you can insert yourself in". I'll let that one sink in.
Kuu-Pillow's box asserts in English:
Feels good. Feels right. Kuu-Pillow not only feels great, it's well-made, durable, functional, and it feels right with new and experienced users alike. With Kuu-Pillow, we strive to satisfy and not dissapoint [SIC].
Why is it that some of the best English I've recently seen on a Japanese product happens to be on a sex toy?
Kuu-Pillow is an inflatable, vinyl pillow that has an opening that can be outfitted with a fleshlight type sex toy and then covered with your favorite hug pillowcase. In the middle of the pillow, you can put a two-liter bottle to keep the pillow in place. That's for when you sleep soundly next to it, no doubt.
The reaction online in Japan has ranged from "Talk about pathetic" and "What's wrong with this country?" to "I'll take one!" Keep in mind that this pillow appeared on an adult goods site, and it's certainly not a mainstream product—it's not even a mainstream product among otaku.
While recently dakimakura have become closely associated with Japanese nerds, it wasn't always that way, and the word itself doesn't immediately have a geek connotation. Japanese website Daki-makura.com, for example, has an array of hug pillows, but it's not pandering to otaku. The site is actually targeting folks, especially women, who want a better night's sleep—not this.