Well... no-one really quite knows. Some believe that they originated in China, as crocheted or knitted dolls have been around for centuries but in fact amigurumi have only been around since the last 10 or 20 years or so.
The Japanese craze for everything cute began in the late 1970s really as a marketing tool. It was believed that the vast majority of people watching television during the day or off out shopping were women and it was believed that if a product was made cute then it would sell. And it worked. Even today you will notice in Japan that cute creatures appear on almost everything, even serious objects such as warning signs or political notices. You may even recognise some of them too such as Hello Kitty or Miffy. It was thought that if something was made cute, then it would get noticed.
In the 1980s the news channel NHK ran a show titled Ami and the amigurumi craze was believed to have been born around that time.The term 'ami' means crocheted or knitted and 'nuigurumi' means stuffed doll.
The Japanese suddenly realised that they could take this cuteness craze to a new level and make their own adorably cute dolls. The craze has grown ten fold too with people all over the world now wishing to make these adorable creatures, collecting them and designing ever new bizarre combinations.
So what defines an amigurumi? Well, amigurumi are typically animals but can range from all types of creatures such as mushrooms through to raindrops, there really is no limit to what you can create but the key ingredients are their human like anthropomorphic features of an over-sized head on a cylindrical body with undersized arms and legs.
You got this part designed then you're well on your way to making your first amigurumi!