Clowns are terrifying on their own, let alone combined it with man-eating, nihilistic Ghouls. That's exactly what Tokyo Ghoul's Clowns -- Piero in Japanese -- faction was. But, despite playing a large role in the series' events, not much is known about them.
Even the CCG's database has very little about the Clowns. What is known is that they, like most Ghouls, primarily wear masks and had the goal of "having the last laugh." They also had at least one member who was an associate of another faction. Beyond that, nobody knows what that goal means, where the group's active areas are, and how many members are involved. However, two members in particular have major roles in the series' plot.
The founder of the Clowns was a Ghoul named Roma Hoito. While embodying a clumsy, unimpressive persona at Anteiku, her true personality was sadistic and carefree -- but not in a good way. She found joy in human trafficking and destruction. Much older than she looks, Roma grew up without parents and had to fend for herself, often eating rotten flesh to survive. At the age of seven, she killed her first human, then began eating other Ghouls to take over their territory and cure her boredom.
She became well-known amongst the strongest Ghouls and mass murderers, getting the name "Dodgy Mother" from the CCG. Eventually, she formed the Clowns in response to how she viewed humans and their society. She saw them as weak and insignificant, yet they were happy. She wanted to kill them and get a rise out of them. Ranked as SSS, she fought Tsuneyoshi Washuu -- Nimura Furuta's father -- and lost against him, an achievement that bolstered his rise through the CCG.
Roma was eventually detained at Cochlea, and was surprisingly happy with her solitude. The CCG, and even the Clowns themselves, had no clue about her identity as the leader of the Clowns, and gave her the new codename "Gypsy." She escaped during the Second Cochlea Raid after being attacked by Aogiri Tree's Tatara. Sometime later, she went to see Uta at the HySy ArtMask Studio, where he offered to get her a part-time job at Anteiku in order to meet Kaneki. After the Owl Suppression Operation, she celebrated the rumored death of Kaneki but instantly recognized him in disguise later as Haise Sasaki.
She took part in the Auction at Zeum Hall, taunting the human trafficking victims. She fled with Uta during the raid on the Auction and resurfaced on Rushima where she attacked Nishiki Nishio. She was knocked into the air by Kurona Yasuhisa and was then captured by the two. She remained in captivity until Nico told her to pick a time to escape. He wasn't there to receive her though. Roma was then seen helping in killing investigators who were against Kichimura Washuu. It was during this coup that she was killed by Kuki Urie, her head decapitated and impaled.
Known as "No Face," Uta was one of the friendlier members of the Clowns. The owner of the HySy ArtMask Studio, Uta used to be the leader of the 4th Ward, the strongest Ghoul there. It was there that he befriended Renji Yomo. Uta meets Kaneki when he and Touka Kirishima arrive at his store to buy a mask for Kaneki. He brings the mask to Anteiku after Kaneki finishes his training, and makes him try it on, remarking the reason he put the eye patch on the right side was the left one was less seen. Despite previous friendly interactions with Kaneki, Uta celebrates with the other Clowns at the news of his death.
Uta is shown throughout the series as playing multiple sides, but ultimately allies with Roma and the Clowns. He has an unhealthy fixation on his friend Yomo and states that his main purpose in living is to kill and devour him. He helps rescue Kankei at several points in the series, including after the Dragon incident. He gives Kaneki advice but hides a manipulative and sadistic personality.
The series never really gives fans a real insight into what the Clowns' ultimate goals are. It only touches on the individual Clown members that have the most impact on the story. It's safe to say, though, that the group revels in destruction and mayhem. That may be all they really want in the end.