Pilsen is how you pronounce PLZEN. It's a town in the Czech Republic where pilsner beers were born in 1842.
Pilsner on the other hand, the -er is a masculine suffix which generally means "from". A Pilsner beer is from the town or region of Plzen. Likewise, a male from Plzen is also called a Pilsner, while a female from Plzen is called a Plznerine (-ine being the diminuative/feminine suffix).
As for beer, it is the style of beer brewed in that region.