Advanced Power Management (APM) is a Power Management system. Configuration and control is handled by the BIOS. It is considered obsolete and has been succeeded by ACPI (which Linux can handle quite well).
Normally ACPI is preferred to APM, but sometimes there can be problems with ACPI (often caused by bugs in the ACPI table firmware). In these cases, since most current systems still support it, APM can be used instead. Also note that ACPI doesn't yet add many new features compared to APM.
In Linux, support is provided either by the apm module or else APM can be built right into the kernel.
If you are trying to get APM working, make sure your kernel's ACPI support is disabled. Accomplish this either by giving the acpi=off argument to the kernel (if ACPI support is compiled in the kernel) or by making sure the ACPI kernel modules don't get loaded. (Note, you use your bootloader to pass options to the kernel at boot-time.)
APM itself can also be enabled/disabled with an argument to the kernel (apm=off).
To find how if you have ACPI or APM support look in your bios or run "dmesg".