The major historical reference here is to the political machine in Chicago.  During this era, political machines dominated the politics of many big cities.  Chicago's was a very strong machine that lasted much longer than most cities' machines.

Machine politics was based on the idea that, as the book says, if you worked for the machine, it would pay you back.  People worked hard to ensure that their neighbors would vote the "right" way.  In return, they got jobs for themselves and patronage jobs for some in their neighborhoods.  They were able to get favors from the government.  

In general, machines tried to help the poor and immigrants to some degree in exchange for their votes.  They used the power they got through winning elections to become corrupt and enrich themselves.