This style is derived from the colloquial French term béton brut, which does not have a direct English translation, but can mean either "cement is cheaper than glass", or "lots of poured concrete with no concessions to æsthetics or windows." Brutalist architecture was especially popular in the 50s as an anti-Dada backlash against neo-classical style of the 20s and 30s, but it is generally considered to be a subset of the larger Soleil Mauvais movement that emerged from the eastern European Soviet Bloc nations of the era. One of the features that separated Brutalism from other schools of architecture was that Brutal buildings were designed by anonymous committees, rather than individuals. This committee design usually resulted in ugly, bland façades juxtaposed against classic Rococo or Modern architecture. It also lent itself to curiously angular design, and rooms tacked onto the outside of the building like an afterthought (such as Boston's city hall as pictured below).
These buildings were popular in eastern Europe for a number of reasons. The Soviets found that the hard, utilitarian look of the buildings tended to pacify their citizens by sapping them of all hope and suppressing the urge for independent thought. The flight of many skilled glass artisans to the west after the invasion of Hungary also led to a broader adoption of mostly-windowless buildings as glass came into short supply. Finally, the unfriendly face of the building discouraged citizens from entering them and bothering busy civil servants in their work since there was a general - and not entirely inaccurate - perception that entering the building was often a one-way journey, especially when you were entering it with police assistance. The Russian term for this architecture was вечная пытка, which translates roughly to eternal torture.
There is a common conception that this style became popular in Winnipeg because Ukrainian refugees to the city missed living in constant fear, and strove to recreate a bit of Kiev in their new home. While there may be some truth to that, a more likely explanation is that people discovered that removing windows from a structure meant that you could enter a building and for a few golden hours, almost forget that you were in Winnipeg. Perhaps the mostly likely scenario was that these buildings were a result of machinations by the powerful Concrete Lobby that held a lot of sway over the city's design and approval committee.
Anyway, there has been some talk lately of tearing down the Public Safety Building and replacing it with - well, anything really. A bunch of people are up in arms about that because this is apparently a good example of an architectural style that is disappearing as cities around the world realize just how ugly some of these buildings are. As much as it pains me to say it (especially since this building feels like herpes of the eye every time I drive by it), I agree with the preservationists, but not for the reasons that they would like. I think we need to keep this building as a warning to future generations. It can be a benchmark of awful against which we measure all future buildings. "Well, it may be ugly, but it's no Public Safety Building."