Continuous Data refers to data that is measured on a continuum. It is data that is measured on an infinitely divisible scale (e.g., time, weight, and temperature) such that one half a unit still makes sense; half a minute, half a pound, etc.
A defining characteristic of continuous data is that it requires a gauge or meter in order to be measured (clock, ruler, scale, thermometer, odometer, etc.).
Note that Continuous/Variable Data is the opposite of Discrete/Attribute Data, which cannot be infinitely divided and still make sense.