Literally: “wise shitter” / meaning: know-it-all
Klugscheißen is a real national sport in Germany. It is impossible to tell a group of Germans at 12:05 AM that you will meet again tomorrow—without one of them replying with a self-satisfied grin that “technically” it is today already.
Apart from Klugscheißer, there are some other words to describe people who constantly want to make you feel like they are smarter than you. Besserwisser (“better-knower”) is a good alternative, as well as Oberlehrer (“uber-teacher”) or Rechthaber (“right-haver”). With that many options, you will find the right one for every situation.
In one regard, however, a German is usually much less of a Klugscheißer than, let’s say, a Frenchman. It is rather unlikely that Germans will bug you with correcting your grammar while you talk. That’s not necessarily because they are trying to be polite—but maybe also because many native speakers cannot fully cope with their subjunctives and complicated inflections themselves.