Characteristic frequency in RLC circuits refers to the natural frequency at which the circuit oscillates when not damped. The damping ratio indicates how oscillations in the circuit decay over time, with overdamped circuits returning to equilibrium slowly, underdamped circuits oscillating before settling, and critically damped circuits returning to equilibrium as quickly as possible without oscillating. To achieve specific damping conditions, one must adjust the values of resistance (R), inductance (L), and capacitance (C) in the circuit. The method involves calculating the damping ratio using the formula based on these component values. Understanding these concepts is essential for analyzing the behavior of RLC circuits in various applications.