A denomination is one named church family — Catholic, Baptist, Presbyterian, and so on. Non-denominational means the thing is not tied to one of those named groups. You hear it most with churches and some schools: they still talk about God and faith, but they do not say “we belong to this one official church brand.” A non-denominational service is meant to feel open to people from different church backgrounds, or to people who do not want a label. Though actually, it does not mean “no religion” and it does not mean the people have no beliefs; it only means they are not flying one denomination’s flag. The word is a bit formal and mostly sits in church, school, and wedding language.