In electric field how we define high potential and low potential and why the electrons...

High potential therefore equals high voltage, and low potential equals low voltage. A high potential has the power to harm or kill you, create significant property damage, or give you the strength to carry out a lot of labor, like operating a big motor. You wouldn't be significantly affected by a low potential, and you might not even be able to feel the current it would create when you touched it. Low potentials often do not have enough energy to accomplish much work, although there are certain outliers, like a vehicle battery, which can briefly create several horsepower.
Regarding the second component of the question, The only consideration here is custom. It is the underlying idea that we adhere to. And although while your course syllabus mentions Maxwell's equation, its explanation goes beyond that.