Despite his imposing figure and his past reputation, Kuma is a very calm and quiet person. In addition to his demeanor, he can also be seen as somewhat of a benevolent character, especially compared to the other Shichibukai. This assumption can be reached through some of his actions, specifically when he spared the lives of the Straw Hats on two separate occasions. 
Although he obeys the commands of the World Government, Kuma disagrees with what his superiors deem "good" and "bad" in the One Piece world. Instead, Kuma strives to uphold his own ideals (described as "Moral Justice”) whenever possible. He even goes so far as to imply that Blackbeard's acceptance into the Shichibukai ranks had been a poor decision by the government, despite the fact that it filled the position left by Crocodile's defeat.
However, Kuma's loyalty does not extend to the Marines. This can be seen when he refuses to answer a direct question from Admiral Kizaru during the Sabaody Archipelago Arc. Due to his unwillingness to aid the Marines without a direct order, Kuma didn't hesitate to lie when it came to his victory over the Straw Hats at Thriller Bark.
When talking, Kuma customarily uses the word "target" in his sentences. He also tends to ask a person where they would like to go on a trip before he sends them away with his Devil Fruit's power.
There are still several mysteries behind Kuma's character. The story behind his transformation into a "Pacifista" and what exactly it entails is still unknown, though Doflamingo tells Emporio Ivankov that the "Tyrant Kuma" he knew was dead. He also whispers a message to Rayleigh during the battle at the Sabaody Archipelago, which the old pirate believes puts the other man at risk.  The message given to Rayleigh has yet to be revealed.
World GovernmentUnlike the other Shichibukai, Kuma is the only one who is loyal to the World Government. For this, the World Government values him greatly. Moria admits that, because of this allegiance, Kuma worries him more than any other Shichibukai.
Marines“ We (Shichibukai) have no obligation to cooperate with the Marines save where the government is directly involved... Your question shall remain unanswered.
— Kuma's response to Kizaru's demands.
While Kuma follows the World Government, he has no allegiance towards the Marines. Only when he has been given direct orders by the World Government to work with the Marines will he do so. Without such orders, he has no obligation to cooperate with the Marines regardless of the situation.
RevolutionariesKuma seems to have had some past with the revolutionaries. He in particular seems to have had acquaintance with Dragon and Ivankov. His exact relationship with them however is currently unknown, but he is no longer the man they once knew him as.
Straw Hat PiratesKuma was ordered to kill the Straw Hat Pirates after Moria’s defeat at their hands. However, he has spared their lives once at Thriller Bark, and again on Sabaody Archipelago, when he helped them escape Kizaru and Sentoumaru.
While Kuma helped the entire Straw Hat crew, he has shown a certain respect for Zoro, specifically after he finds the swordsman alive following the events at Thriller Bark. Zoro, too, recognizes and respects Kuma’s strength, admitting that he is only alive because of the other’s mercy.
Kuma also knows a lot about Luffy, as he at least knew that Portgas D. Ace and Monkey D. Dragon are his adoptive brother and biological father, respectively. Both relationships were not public matters, and as such, very few people actually know about them, until Sengoku made it public during the war.
Abilities and PowersKuma is one of the few people to have completely defeated the entire Straw Hat Crew, having done so twice; he is also the only character introduced so far that has defeated the crew single-handedly. Although, the crew was extremely weak both times and they were in no shape to fight another battle, much less a Shichibukai (they recently battled other Shichibukai Gecko Moria, as well as a island full of zombies, and Oars, and in the second time, battled against a large amount of Marines, PX-4, Kizaru, and PX-1). However, he doesn't seem to want to permanently injure the Straw Hats either, having spared their lives twice, indicating he may have held back.
Devil FruitKuma ate the Nikyu Nikyu no Mi, making him a "Paw Paw Man". This Devil Fruit gives him paw pads which give him the power to push anything, including the air around him, at the speed of light. Kuma fights in a style reminiscent of sumo-wrestling. He crouches low in a wide stance, even using the signature stomp, and attacks with open-palm strikes, using his special paws to launch air bullets. Much in keeping with the sumo inspiration, Kuma spends almost all of his time with his feet planted, refusing to give his ground.
The fruit's powers also allows him to move at the same speed as the objects he pushes, possibly by using it to push himself, appearing instantaneously at a desired location regardless of distance, all the while he moves no more than a slow walk. Some mistake this as a form of teleportation.
Kuma is a cyborg modified by Dr. Vegapunk. However, he is different from and is much stronger than Franky. His body is able to withstand most attacks, including Sanji's kicks and even the attack of Zoro, which was able to cut through steel. Zoro could only leave a scratch on Kuma with a surprise attack. With his modifications, he is an incomplete weapon of the World Government.
As a Pacifista, Kuma has a laser launcher, which not only causes massive explosions upon detonation, but can also melt steel. This laser is apparently a copy of Kizaru's Pika Pika no Mi powers. For Kuma, this launcher is only installed in his mouth. For the other Pacifista, the launcher is also installed on their palms as well. This aspect, along with Kuma apparently having free will, makes him different from the other Pacifista as he has his paw pads instead of laser holes.