A way of powering the tiny preamplifier in a condenser microphone. Phantom power is a DC voltage (between usually 11 and 48 volts) that is applied to pins 2 and 3 with respect to pin 1 (ground) on an XLR cable. The voltage is usually supplied by the microphone mixer, or a separate phantom power source. The mixer will usually provide current-limiting resistors which prevent a bad microphone from damaging the phantom power supply.
Makes you wonder where the Tragically Hip got the title for their CD from.