Kosher style refers to Jewish cuisine—most often that of Ashkenazi Jews—which may or may not actually be kosher. It is a stylistic designation rather than one based on the laws of kashrut. In some U.S. states, the use of this term in advertising is illegal as a misleading term under consumer protection laws.
Jews who do not keep kosher, but wish to restrict themselves to eating ethnically "traditional style" foods may consider themselves to be keeping kosher style.