Neumünster sits in the middle of Schleswig-Holstein, roughly halfway between Hamburg and Kiel, and has long been defined by its textile and leather industries. The city took heavy damage in World War II and was rebuilt in a practical rather than picturesque style, so do not come expecting half-timbered charm. What you will find is a straightforward working city with a few genuine points of interest.
The Museum Tuch + Technik, housed in a former cloth factory, does a surprisingly good job of telling the story of the textile industry that shaped this city. The old town church of St. Vicelinkirche dates back to the twelfth century and survived the war largely intact. Neumünster also has a decent zoo, the Tierpark Neumünster, which makes for a pleasant afternoon if you are traveling with children.
Most visitors pass through Neumünster on the way somewhere else, and honestly that is a reasonable approach. But if you are driving between Hamburg and the Danish border and want to break the journey, the textile museum and a walk through the compact center will fill a couple of hours well enough.