This means that in addition to the dynamic linker loading libraries at random addresses, in a random order, the offsets inside the library itself are different on each boot, and on each system.
What part? At least for the library randomization, a special libc.so.X.Y.a is part of the base install, objects are extracted with ar(1), and then re-linked in a random order (sort -R/arc4random(3)) to create a working shared library.
OpenBSD's bootloader seeds the kernel, mixing in other entropy sources. High quality random numbers are available very early compared to other operating systems.
See Theo's talk from Hackfest 2014, an updated talk originally given at EuroBSDcon 2014:
Does it actually do the randomisation at boot time? It's unclear from the article, but OpenBSD could be randomising the next kernel to boot after the current one has been loaded. This could be performed some time after the boot process, allowing more randomness, and minimising the boot-time workload/code complexity.
On desktops, Intel Ivy Bridge and newer and everything AMD since June 2015.
On mobile, most mobile SoCs include security stuff, Qualcomm seems to have had them since at least the Snapdragon 805. See here for the addition of the RNG to the linux kernel in 2013: https://lwn.net/Articles/570158/
Even common embedded SoCs like those used in the ESP8266 include hardware RNGs.
Really, there's no excuse for not using it as at least one factor. If you're concerned about possible backdoors, xor it with your own CSPRNG in software like the Linux kernel does.
Recent AMD and Intel systems with AES-NI provide a hardware RNG. Although as far as I was aware this is not used on OpenBSD for fear of hardware backdoors.
https://marc.info/?l=openbsd-cvs&m=149605105003964&w=2
https://marc.info/?l=openbsd-cvs&m=146168291000757&w=2
This means that in addition to the dynamic linker loading libraries at random addresses, in a random order, the offsets inside the library itself are different on each boot, and on each system.
Robert Peichaer (rpe@) added the kernel re-linking at install/upgrade: https://marc.info/?l=openbsd-cvs&m=149884116824098