Both the Zemstva (plural of zemstvo) and their urban counterparts, the Municipal Duma, were two types of institutions for limited local self-government that came into being because of the the Great Reforms. In a nutshell, the tsarist state felt a strong need to modernize its governmental institutions after its defeat in the Crimean War but feared the results would run counter to the interests of autocracy if it modernized too much. Therefore, the electoral systems of both these institutions were rigged to favor the local landed-aristocracy who had a clear stake in upholding the tsarist empire. The zemstva also had very little power to counteract the authority of the empire's central administrators such as the provincial governors or the local military units. The Zemstva did have enough power to improve roads, city buildings, and (most importantly as far as St. Petersburg was concerned) collect taxes. By giving some degree of local authority to zemstva and duma (which were elected city councils), the hope was they would make the Russian state more efficient and modern while preserving its traditional character.

More detailed answers about the Great Reforms are here and here

Could I also get an example of a government that works similarly today?

Just a reminder to OP and potential respondents that present-day politics are off limits in this sub. Per the "20 year rule", do confine responses to pre-1995. Thx!