Cloning (going by several names, like Kage Bunshin / Shadow Clone similar to Naruto) is a technique first witnessed in Kageto Kinoshita, who uses it to run the Southern Tokyo Branch of Pantasia while all the other employees slack off to compete in tournaments or come up with new dishes (a running theme).
While initially, this is played off as a joke (and could be taken as Kageto simply moving at high speeds, or showing multiple instances simultaneously), it becomes clear as the anime progresses that this is a real ability. This comes to light when Bolneze uses the ability to judge many dishes simultaneously.
The cloning ability is also demonstrated in the second opening in the anime, as both Bolneze and Kageto are shown in sequence using it.
Bolneze invented the ability himself (according to his recollections) while Kageto apparently learned it from the Kinoshita Circus since he was from a circus family.
Kageto himself is a master of copying (able to copy others' dishes with over 95% accuracy) so his cloning power may be linked to this, as he is able to literally copy himself.
Kageto later uses the ability to entertain the public by having several of his shadow clones prepare bread on the street for passerby.
Kageto has remarked that using the clones is very exhausting. This is a similar concept to Naruto where it uses a lot of ki.
In other anime, this ability has shown up in Akazukin Chacha where Orin the Ninja girl uses it against opponents. It has also shown up in the game Disgaea 2 where Yukimaru and her older brother use it as their ultimate ninja attacks. In this respect, the circus folk of Yakitate are similar to ninjas.