APIC is the Advanced Programmable Interrupt Controller. It's the thing on the motherboard that controls which INTA, INTB, etc. line (from the PCI slots) gets assigned to which IRQ number from the CPU's perspective. Ideally, all PCI cards (and yes, this includes AGP) would use INTA, and each slot would be mapped to a different IRQ number, but that's not always the case. Anyway, newer APIC's (like the IO-APIC) allow more than 15 IRQ's, too.
ACPI, OTOH, is an interface to power management, PnP BIOS, and a bunch of other things. The only problem with it is that support is currently "experimental and incomplete", according to the help for the option in menuconfig.