Overriding, in this sense, means more important than anything else you might put beside it. People talk about an overriding aim, an overriding concern, an overriding need: the thing that wins when two wishes pull different ways. Safety can be the overriding concern; getting home for a funeral can be the overriding reason for a sudden trip. It is a slightly formal adjective, common in serious writing, news, and school essays, less common in casual chat, where people might just say “the most important thing.” Though actually, this is not the everyday verb override, as in cancelling a vote or a computer setting. Same picture — one thing sitting on top of another — but here you are ranking importance, not wiping out a rule.