A South German state, and for many the quintessential German state - which is kinda ironic, as Bavaria is the one German state which insists on maintaining its own regional identity. Also quite annoying for non-Bavarian Germans when they are defined by clichés derived thence. Bavaria is sometimes described as Germany's equivalent of Texas, a place where clichés live: wheat beer, sauerkraut, lederhosen, the Oktoberfest, fairy-tale castles…
Historically, Bavaria is the only one of the old German tribal duchies of the Early Middle Ages to survive, becoming a powerful mediaeval duchy - but at first no electorate. This was because the Bavarian ruling House, the Wittelsbachs, also held the Palatinate and nobody wanted one house to control two votes. This was rectified after the 30 Years War, and during Nappy's wild rambling through Europe Bavaria also became a kingdom.
See also Bavaria in other timelines for an alternate history look at Bavaria. There is an interesting view in Alternate History that Bavaria is ready to secede at any point in history at a whim. This is usually connected with some weird explanation involving regional denominations, even those had hardly a place in German politics ever since the end of the 30 Years War anymore. See also the Disunited Germany cliché, of which this could be considered part.
A further common misconception is that all of southern Germany is Bavaria - which completely ignores Swabia.