In a standard low-impedance microphone connection, the audio signal is carried through a cable to a three-pin XLR connector that plugs into a preamplifier. Pin 1 is ground, and the audio is a balanced AC signal on pins 2 and 3. (When pin 2 has a positive voltage, pin 3 has the same negative voltage.)
To apply phantom power to the microphone, the preamplifier raises both pins 2 and 3 to the same DC voltage, typically 48 volts or less. This DC voltage powers the microphone without interfering with the AC signal carried on the same wires. (Instead of balancing out to zero volts, pins 2 and 3 balance out to 48 volts.) Both the microphone and the preamplifier use simple electronic filters to separate the AC and DC voltages.
Phantom Power is also the name of an album by the rock band The Tragically Hip.