Talking about parasitic elements in an circuit.
This is the explanation that I would have given, as well. In this type of application "order" is talking about the exponent of the unknown in the math description of the circuit. So a circuit with only resistance is first order, with either capacitance or inductance would be second order, and if it has both capacitive and inductive reactance then it is third order.The order of a system usually starts with the number of reactive elements. A system with a capacitor and an inductor is a second order system. Now imagine what would happen if the inductor had a parasitic capacitor in parallel with it. Now your second order system becomes a third order system.
Circuits with only resistance are order 0, because there is no frequency dependence. Order 1 systems have either a capacitor or an inductor, but not both, The frequency dependence is 1st order. And so on.This is the explanation that I would have given, as well. In this type of application "order" is talking about the exponent of the unknown in the math description of the circuit. So a circuit with only resistance is first order, with either capacitance or inductance would be second order, and if it has both capacitive and inductive reactance then it is third order.