Amigurumi is a Japanese word simply meaning knit/crocheted toy. Basically amigurumi are stuffed animals, dolls, etc which is made by knitting/crocheting the form of the toy and then stuffing. The method of making these toys is not Japanese at all; however, those that knit or crochet often use the word amigurumi simply because saying something like 'a stuffed, crocheted cat' is a mouthful.
Amigurumi are usually worked in the round, which means instead of working back and forth like you see in afghans and sweaters, you work around and around. Amigurumi have very few if any seams; often the only stitching involved is the attaching of limbs. They come in as many shapes and sizes as any other soft toy, and are gaining popularity with both handicrafters and toy collectors of all ages.
I crochet, not knit, so the only example pictures I have are of crocheted amigurumi. I can't knit something that doesn't look like a cat chewed it to save my life! However, if you search for images under amigurumi, you can see many different types. Some are really creative, like an amigurumi Spock^^
An amigurumi Curious George. He's over 60 cm (two feet) tall, and does NOT have a tail. Curious George is a rather odd monkey like that^^
A mouse amigurumi, roughly 10 cm (4 inches) tall