A campaign is a number of adventures tied together into a bigger story arc. Campaigns can be designed to consist of many adventures, or as few as a single super adventure.
Many published campaigns are available. Some published campaigns are standalone campaigns, allowing a Dungeon Master to start one where another leaves off, in any level appropriate sequence. An Adventure Path, on the other hand, is a lengthy campaign consisting of adventures published sequentially in serial format, such as in Dragon magazine, designed to be played from start to finish. DMs can also opt to run a homebrew campaign of their own invention.
A campaign setting is even broader than a campaign. A campaign setting describes an entire world in which to build campaigns.