IDE is a legacy controller used for old hard drives and old Operating Systems.
AHCI replaced IDE. Set it as this unless you are going to use RAID.
RAID is used with hard drive arrays and comes in different flavors. For instance RAID 0 allows you to combine two drives into a single partition and increase performance. RAID 1 mirrors data between two drives so if one fails you have an identical copy. RAID 5/6 are examples where you have an ARRAY of many drives and can often take multiple hard drive failures. It is used in servers.