At its best it means interested in politics and government; trying to make a changes in public policy, laws or the government working to get an official elected, or lobbying to have legislation passed, collecting petition signatures. It can also mean a person trying to change things for their own benefit, to gain status or power in the workplace. It can also mean someone who is a nuisance, constantly wanting to change things and who interferes in matters that are none of their concern. At its worst it means a total fuckwit like
Russell Brand a
self-styled activist for whom
politically active means espousing views that the majority of people find repugnant or ridiculous.