AHCI stands for Advance Host Controller Interface. It is a newer technology to provide advanced features to the Serial ATA standard. It allows for access of the native functions of the SATA interface such as Native Command Queuing (which allows greater performance by optimizing how controller requests data from the hard drive) and hot swappable of SATA devices so that you may remove SATA drives from your PC without first having to shut down your computer.
In order to use Windows with the AHCI features enabled, you will need to specify an AHCI driver for your stoage drives to be recoginised as an usable root hard drive.
IDE mode is designed to give the greatest amount of compatibility with older operating systems. If your operating system is not detecting your hard drive it is likely that you will need to specify your AHCI / RAID drivers, or enable IDE mode of the SATA controller.
AHCI mode requires unique drivers. For MOST operating systems you will have to specify the AHCI drive to be able to install to a AHCI hard drive.
All motherboard chipsets released after 2011 have support for AHCI
Most of the nforce 7 series motherboards do not support AHCI on the nvidia ports. However, the 730i and 730a have support for AHCI.
None of the 6 series motherboards have support for AHCI. Lastly the H55 V does not have AHCI Support.