In Brazil, the expressions "administração pública" and "poder público" are often used in the sense of "government" and should be translated as such. "Administração pública federal", for instance, should be translated as "federal government".
There are multiple definitions - click on the translation that matches your context.
the implementation of government policy (=making plans and ideas developed under government policy start to work and to be used)
She is a professor at the University's department of politics and public administration.
(the public administration; the administration) the people whose job is to implement government policy
Food services and retail are expected to create employment while public administration and manufacturing shed jobs.