What is meant by locked bootloader? Everyone complains about locked bootloaders on phones.  From reading the bootloader seems to be code stored on the partition which /boot is mounted.  Once the phone is rooted why couldn't one just delete what's on /boot and put their own stuff there.  When you do an OTA and it update the boot loader I assume it just writes files to this partition.

In a Linux distro I can replace grub which is stored in boot with LILO or whatever by simply replace the files in /boot and write the PBR to the head of that partition to then boot into LILO.  When the PC boots it looks at the MBR which tells it to look at the active partitin (persumably the one with /boot), chain into that and read the LILO code at the head which then does stuff with all the other files in /boot.

How do android devices boot differently that prevents that?
The bootloader is not generally on the /boot partition, it's on a separate one, although that's not really the crux of the issue.

The problem occurs when the bootloader is cryptographically signed, which is intended to prevent you from replacing it with your own. The device will check the signature of the bootloader at startup and refuse to boot one with an invalid signature. After that, the bootloader checks the signature of whatever is in /boot, refusing to boot that if it's not signed validly. Therefore, you can't overwrite either partition without rendering the device unbootable.

When a bootloader is unlocked, it will not check the signature of the other partition images, which is why you are able to install custom ROMs. This means that you don't need to replace the bootloader in order to modify /boot, you just need to unlock it so that it skips the signature check on /boot. If the bootloader is locked and signed, then you're essentially stuck, barring an exploit that allows you to bypass one of the signature verification steps.

This also means that locked bootloaders, in and of themselves, are not necessarily a problem. The real problem is signed bootloaders that do not provide an unlocking mechanism.

The process is (more or less) analagous to UEFI Secure boot, although it's probably not exactly the same architectural implementation. Incidentally, going with your example of Linux, one of the primary criticisms of UEFI Secure boot is that it could potentially be used to prevent installation of alternative OSes on traditional PCs via the same signature checking scheme.