I'm running Kubuntu 12.04 on 32 bit and the updater offers a security update 'Linux kernel headers' and 'Linux kernel image for version 64 bit x86 SMP'. Should I install this? And if not, why do I get the offer?
Check whether your OS is with PAE extension.
Most dekstop/laptop processor made in past 10 year support PAE.
Since Ubuntu 10.04 and newer support PAE out of the box so it can access 64 address line.In 12.04 its default.
Probably that's why you got that kernel image.
Unless you have modified your kernel or using the kernel for system software development,its safe to install kernels provide via