Campaign is trying to do something. Some battles in wars are called campaigns. The word comes from "Campania", a region where the ancient Roman army often fought.
When someone in politics seeks election to a political office, that is called a "political campaign". Sometimes, a series of advertisements can be referred to as an "advertising campaign". A "blood drive", when the Red Cross or a hospital asks people to give blood, is also a campaign.
A campaign usually involves groups of people following a plan and working together in different ways to get what they want.