Residential schools were schools set up by the Canadian government to assimilate First Nations children into (predominantly WASP, and in Quebec, French Catholic) Canadian culture. They were one of the most damaging acts perpetrated by Canada on a minority group, along with the internment of Japanese-Canadians and the Chinese Exclusion Act. The effects these schools had on First Nations communities are still felt (and largely ignored by non-aboriginal Canadians) today.
The first residential schools opened sometime around the 1840s and chillingly, the last of them closed in 1996. They were initially founded by churches, some 60% of them being Catholic and most located in central and eastern Canada.
The specific origins of the program are hard to date, because many of the institutions that eventually became residential schools didn't start out as such and there was never a specific act passed by legislature(s) outlining a specific policy for educating First Nations youth.
While laws such as the Gradual Civilization Act and the Gradual Enfranchisement Act set laid the groundwork for policies designed to assimilate First Nations youth into white culture, the residential schools were part of an ad-hoc policy that enjoyed wide support from Canadian politicians during the late nineteenth century.
The basic idea behind the institutions was to "kill the Indian, save the child."
Least you think this was a strictly Canadian problem, our neighbours to the south were engaged in similar practices as were Australia and New Zealand; South Africa also engaged in the most infamous of these policies.
There is a damn good reason as to why the residential school system is a terrible thing: the conditions were appalling at best and living in them was only made worse by the horrendous treatment of the faculty and staff unto the students. Students routinely suffered abuse in every one of its forms from racial slurs, verbal scathing, corporal punishment and sexual molestation. They were taught either implicitly or directly that their cultural roots were shameful and filthy, that they were cursed with a lack of "civilization" and that pretty much the only way to save themselves is be more culturally white.
On top of that, students were kidnapped from their parents and villages and forced to attend these institutions. Think of it as being kidnapped by fundamentalist Christians that are bent on converting you not only to their faith but into their gene-pool, with some lessons in math, civics and Jeebus thrown in for good measure.
Near-term, graduates of these schools returned to these families as shadows of their former selves. They were incapable of fitting in with their communities and couldn't properly perform any of the communal rites associated with their old lives as it caused much anxiety and conflict with the "lessons" they learned at the residential schools. Graduates also took to drinking (later drugs), crime and/or suicide to forget the things done to them. Paradoxically, the program notably failed wholesale to produce any functional and productive members of white Canadian society from aboriginal communities.
Long-term effects were at least successful in achieving the goal of the total destruction of First Nations communities. Social disorders and behaviours acquired from the torture experienced in residential school system were replicated by successive generations leading to the collapse of the communities on Indian reservations. Even today, first nations persons are overrepresented in prison; have high rates of teen pregnancy, substance abuse and suicide; are less likely to find employment or hold down a job and are way less likely to obtain credit than non-aboriginal Canadians.
The Canadian government has been very slow to acknowledge its part in the abuses and continues to drag its feet to this day. There have been a few bright spots throughout history (such as the apology from the Canadian government for their tacit endorsement of this policy), but little in the way of seriously addressing the imbalances between the first nations experience and that of the rest of Canada. This is partly due to the long history of failure by Canadian governments to seriously redress issues and the resultant mistrust of aboriginal Canadians towards the Canadian government.
White Canada largely fails to comprehend the issues faced by the first nations community, still holding onto a lot of racist views of them; most notably, that the First Nations communities have somehow brought their misfortune onto themselves. To this end, they elect leaders that hold this view perpetuating the cycle yet again.