Phantom power (also written as +48V) is a method of delivering electrical power to condenser microphones through the same XLR cable used for the audio signal. It was standardized at 48 volts DC by the IEC 61938 standard and is built into virtually every modern audio interface and mixing console.
Condenser microphones require power to polarize their capsule — the electrically charged plate that converts sound into an electrical signal. Without phantom power, a condenser mic produces no output at all. Dynamic microphones like the Shure SM58 do not require phantom power and are unaffected by it being switched on.
On your audio interface, phantom power is usually enabled by a button labeled '48V' or '+48V'. It is safe to leave phantom power on even when using dynamic mics. However, avoid connecting or disconnecting mics while phantom power is on, as the surge can sometimes cause a loud pop through your speakers.
Ribbon microphones are an exception — older ribbon designs can be damaged by phantom power. Always check the manufacturer's specifications before enabling phantom power with a ribbon mic.