The image itself appeared in print at page 144 in E. D. Morel's King Leopold's Rule in Africa (1903), one of a number of works he put out or oversaw to publicize the forced labor, mass killing, and simple brutality of Leopold's rubber-extraction system in the Congo Free State. The man's name is Nsala of Wala village, and the appendages belong to his daughter, Boali. The photo was taken by John Harris (I believe a missionary), and Morel described the scene as something highly macabre: rubber sentries shot his wife and children, and reputedly had a 'cannibal feast,' with this all that was left behind. Presumably this was punishment for not making quota, or simply the acts of the sentries and the company agent gone wild with power; the letters from a Mr. Stannard at the back mention this attack and suggest it was the latter, because the rubber quota for that period was not due in for several days yet. (See pp. 442-450.)

In other cases where this was done, however, this was absolutely direct punishment, a message that could be sent without necessarily killing the victim, but instead holding them hostage. Hostage-taking to assure workers made the quota of rubber was widespread and routinely abused, with the enforcing soldiers brought from places quite far afield across Africa (and beyond) to perform such tasks when possible. The holders of the hostages, usually soldiers of the Free State (or company rubber sentries so deputized) under a single European commander, would be the ones to sever the limbs or kill a person (depending on what was required). The limbs might be delivered to a person in the family, after they'd been used to confirm that people had been killed or made to pay. (For that latter purpose, such limbs would be smoked and carried in baskets, so as to preserve them--this may be the origin of the cannibal feast motif.) If sentries or soldiers came in without the expected quota of such parts to show their own superiors, they might be punished in turn. The brutality of the whole chain cannot be overstated. It is worth pointing out that sexual violence (rape, mutilation, etc) was also a significant part of this equation, but rarely was commented upon beyond allusion to avoid 'turning off' the public Morel hoped to bring awareness of Leopold's brutality to--yet he does make sure to allude to it. Stories of cannibalism and grotesque savagery, however, played into the moral outrage of paternal imperial 'responsibility' much more effectively, especially when using images of simple fathers who lost children like Nsala. Those were people with whom even an Edwardian-era English reader might sympathize.

Hands and feet (or genitals) could also be presented, smoked, as evidence that punishment had been meted out to villages that resisted the Congo Free State's military police. As for why Nsala would be punished for not reaching rubber quota, that is its own answer. The goal of Leopold's people was to get the most rubber out of the Congo basin possible before new rubber plantations [edit 2: in SE Asia and S America, and some in W Africa, that have their own special horror stories attached later on] came to maturity and the market for rubber--used in pneumatic tires, hoses, and insulation--became crowded enough to drop in value.

Much of this is in Hochschild's King Leopold's Ghost. The original works by Morel (including his major work, Red Rubber) are publicly available online. If you can get a copy of Roger Casement's 1904 Parliamentary report (Cd.1933, "Correspondence and Report from His Majesty's Consul at Boma Respecting the Administration of the Independent State of the Congo")--he was the British consul at Boma, and his investigations gave traction to all Morel had been writing--it's a sobering read. [last edit, I hope: some of the other photos appear in Mark Twain's King Leopold's Soliloquy (1905)--another readily available work in public domain, and one of many that express Twain's disdain for the habits of empire and his readiness to help Morel's Reform Association campaign.]

The ultimate results were a displacement or death of up to 50% of the basin's population from 1885 to 1908--with estimates usually around 8-10 million. It was horrific on a scale that only the industrial 20th century could muster (so far), honestly. We'll never know the full scale, because unlike so many episodes of mass death, Leopold managed to burn most of the detailed records before the Belgian government could get a hold of them.

[edit 1 & 3: Had to flesh out Nsala a bit, and raise the point about smoking the limbs. I don't know if we hear any more about him from the mission letters--although I know Wala village comes up, and he is mentioned, in the appendix Morel points to. I've amended my text to reflect this, and linked the photo's page.]