AHCI stands for Advanced Host Controller Interface. This specification enables communication with an attached storage device. Think of it as a translator, allowing two devices (your host machine and the attached storage device) that speak slightly different languages to understand each other. AHCI mode must be enabled to use Native Command Queuing (NCQ) or Hot Plugging (aka Hot Swapping) functionality as well as Power Management in SATA storage devices.
The Advanced Host Controller Interface (AHCI) is a technical standard defined by Intel that specifies the operation of Serial ATA (SATA) host bus adapters in a non-implementation-specific manner.