Kosher style refers to foods commonly associated with Jewish cuisine but 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 "traditional style" foods while not eating forbidden animals nor mixing meat and dairy, may consider themselves to be keeping "kosher style".