The degree of caution and attention that an ordinarily prudent and rational person would use. In personal injury law, "reasonable care" is the yardstick that's used to determine:
Put a bit differently, in the eyes of the law, a person who fails to act with "reasonable care" in a given situation can be held legally responsible if that failure causes someone else harm.
So, for example, let's say Darcy is driving twenty miles per hour over the speed limit with her vehicle's headlights off one night, when she runs a stop sign. Darcy isn't acting with the amount of reasonable care that's required of drivers. So, any car accident she's involved in will likely be deemed her fault, and she will be on the legal hook for resulting injuries, vehicle damage, and other harm.