Schleswig-Holstein refers to a region on the Jutland Peninsula bordering Denmark and Germany. It is also the name of one of 16 Bundeslands in Germany, bordering on Denmark and the North Sea and the Baltic Sea. The Danish name for this region is Slesvig, and the part of this region that is on the Danish side of the border is part of a region known as Sønderjylland.
This region was the subject of a territorial dispute between Denmark and Germany during the 19th and early twentieth centuries. Because of the mix of Danes and Germans who lived there, the problem was considered intractable by many. Lord Palmerston said of the issue that only three people understood the Schleswig-Holstein question: one was dead, the other in an asylum and the third was himself, but he had forgotten it.
The German state of Prussia, with the help of Austria, acquired the territory from Denmark after defeating the Danes militarily in a short war fought during 1864. After World War I, Denmark reacquired part of that territory after a referrendum in the region; the rest remained with Germany.
See the state's own website, http://www.schleswig-holstein.de/