Today there are no elections in the state of Bavaria, but there are elections of the Landtage in Baden-Württemberg, Rheinland-Pfalz, and Sachsen-Anhalt.
The outcome will also determine the Ministerpräsidenten of these German states (we have in total 16 states in Germany).
The German states are then represented in the Bundesrat which needs to approve (or can disapprove) decisions taken by the Deutscher Bundestag.
Therefore, the outcome will be very important also for Germany.

Because of the refugees crisis, the new right-wing party AfD might be quite successful. Very likely this will be the main topic also tonight after the publication of the results – and in the next days in international media, too.

For those who speak German here is a good overview (in each section of this article you can click on „Landtagswahl in …“ and read a long article about that German state):
http://www.merkur.de/…/landtagswahlen-2016-ueberblick-wahls…

13 million people are allowed to vote, it will also be interesting to see how many people will go and vote. Fewer voter usually means better results for more extreme parties.

PS: Depending on the results of today, I may organize a meeting „Let’s talk about German politics“ at my Little Shop of Science in the next couple of days to clarify upcoming questions.