I think we may need more information. Charles has pointed out the difference as applied to faults. Conductors can also be symmetrical or asymmetrical. A symmetrical conductor will maintain a balance whereas an asymmetrical conductor (cable would probably be a better term) may not. An example would be coaxial cable vs. parallel or twisted pair feed lines. Coax is asymmetrical as the inside and outside conductors have different properties and under certain parameters will exhibit a large amount of line loss. Parallel feed line, on the other hand will not and instead will bare purely resistive losses over a wide range of frequencies and standing wave ratios as it is symmetrical and thus 'self canceling'.
Antennas can also be either symmetrical or asymmetrical. A center fed dipole is symmetrical whereas an off center fed dipole is asymmetrical. Another form of asymmetrical antenna is a ground plane antenna which is usually vertically polarized. A fractal antenna is usually symmetrical in design.
In short, anything symmetrical will have two or more parts that are the same or mirror images of one and other and anything asymmetrical will have two or more parts that are different from each other.