This is the 857th most frequent German word.
bayer
"Bayer" in German refers to a Bavarian, someone from Bavaria, a region in Germany.
The term 'Bayrisches' refers to something from Bavaria, used here as an adjective describing the beer.
Das Bier, das ich gestern getrunken habe, war ein Bayrisches.
The beer I drank yesterday was a Bavarian one.
'Bayer' refers to a person from Bavaria in this sentence.
Ein Bayer liebt traditionelle deutsche Volksmusik.
A Bavarian loves traditional German folk music.
Here 'Bayer' again refers to a Bavarian person, but is used more narratively.