In general, such boot parameters are not needed unless there is a problem with your BIOS and how it handles these standards, or it just might be old enough where these standards were not fully implemented properly.
ACPI (Advanced Configuration and Power Interface) is a standard for handling power management. Older systems may not support ACPI full, so sometimes it helps to give the kernel a hint to not use it. "acpi=off"
APIC (Advanced Programmable Interrupt Controller) is a kind of feature found on newer systems. The "local" version is called "LAPIC". What this controller can do is be set up to generate and handle interrupts, a signal the hardware uses to pass messages. Again, some implementations of APIC can have problems on older system, and so it is useful to disable it. "noapic" and "nolapic".
Sometimes the APIC is working, but it slows things down by getting in the middle of messages being passed around. This can mess with audio and video processing, for example. Folks might disable it for that reason as well.