Lp = 10 * log10 (1/2) = -3 dB
Lp = 10 * log10 (2) = +3 dB
The power (energy) drops to half (1/2).
For voltage, it is sqrt(1/2) = 0.707. When the voltage drops to 0.707*peak_voltage, the power drops to half (-3dB), since the power is proportional to the square of voltage.
Let's say lowpass filter, cutoff frequency is the boundary between the passband and stopband.