A "Mehlspeise" (noun, feminine, pural -n ) is a word used in German cuisine to mean meatless dishes, usually made with flour. It is used most often to indicate a main midday dish which is sweet and grain-based.
The word is not used as much in modern times, but has been known since the 1800s and was defined then as a dish which is mainly made with flour, such as flour soup, mush or pudding. Noodle dishes also count. "Grieß," or semolina, and "Grütze" (puddings thickened with tapioca or semolina) dishes are "Mehlspeisen" as well.
In Germany, outside of Bavaria, it does not mean "Backwaren" or baked goods.
The use of "Mehlspeise" as used in Austria since the 1700s is not limited to flour-based dishes, but is a more general term to mean meatless dishes of all sorts, whether vegetable, egg-based or flour. These could be sweet or savory dishes.
In the 1800s the word started to include the dessert part of the meal, and so was broadened to include Schmarren, Strudel, Schmalzgebäck and Nocken and noodles. It has since been widened to also mean all types of baked sweets.