Mofu mofu (もふもふ) means thick, soft and fluffy: the fur of a big cat, a dog or a rabbit.
A huge fluffy dog walks into the room, and before you know it your hands are deep in its fur. That is もふもふ.
What it means
もふもふ is fur that is thick and soft enough to sink into. It is a younger word than most sound words, made popular online, and today you see it everywhere: pet shops, plush toys, animal cafés.
How to use it
Like ふわふわ, it takes です for the state, and の in front of a noun: もふもふです, もふもふの ねこ. Fans have even turned it into a verb, もふる, “to bury your hands or face in fur”. It is slang, but you will see it online.

みて! この ねこ、 もふもふです!
Look! This cat is so fluffy!

かわいいですね!
So cute!

…ふじさんも もふもふですね。
...You're fluffy too, Fuji.

えっ、ぼく?
Huh? Me?
Close cousins
ふわふわ is light and airy: clouds, pancakes, a kitten's fine fur. もふもふ is thicker and deeper — you sink into it. ふさふさ is thick and bushy, like a full head of hair or a fox's tail. もちもち sounds close but is about food: soft and chewy, like mochi.
In manga and anime
Fluffy animal companions are a favourite in anime, and when a character finally gets to hug one, a blissful もふもふ… usually follows. Fans use the word for a character's big fluffy tail or ears, too.
Can you use it?
Yes, freely: about animals, plush toys, scarves and blankets. It sounds cute and happy. For someone's hair, use ふさふさ instead.