Do as it says and try booting with the no apic option. At the CD boot menu hit F6 (IIRC), append "noapic" and hit enter.
Edit: Your post is a little confusing, though. Did you actually install it or simply boot off the disc and start the error check?
If you have already installed it take the disc out of the drive, reboot your system and if you still get the APIC error you'll need to append noapic to grub's kernel line. To do this:
Reboot the system, hit escape before it counts down to autoboot (you only have ~2 seconds to do this), hit E (to edit), go down to the "kernel ..." line, hit E again and append " noapic" (without the quotes). Finally, hit enter then B to boot the system.
You'll need to make this permanent by editing the grub config (/boot/grub/menu.lst) once you boot into the system.
Edit2: BTW, next time you install Ubuntu (or any distro - thought the way it's done may vary slightly), do the F6 for "other options" at the CD boot menu thing I mentioned above. This way it'll write it to the grub conf for you.