What is a math concept or principle?

"Math concept" is generally used to refer to the "why?" part of answering a math question. Concepts, typically contrasted with facts or skills, are more about how a process works or why it works than the mechanical steps to solving a specific type of problem.

For instance, take an algebraic inequality:

-x < 1

is typically solved by "dividing by negative one and flipping the inequality sign," but that doesn't really explain what's happening.

-x < 1

+x +x

------------

0 < 1 + x

-1 -1

------------

-1 < x

What's actually happening is that we're adding x to both sides of the inequality, which has the effect of "moving" the x to the other side. This doesn't matter in equations separated by an equals sign, but it does in inequalities. Rather than memorizing "flip the sign," a conceptual approach would explain the process this way and help a student understand "why" the sign appears to flip.