Hi omexlu,
depending on your operating system, kernel updates/upgrades automatically remove ( or don't remove ) the module tree of the old kernel, which can lead to issues/errors/problems, if you ( or a script on your server ) unloads a specific kernel - module. To avoid such issues/errors/problems, you would certainly reboot immidiatly, after a kernel update/upgrade.
On Debian/Ubuntu based systems, you would remove obsolete packages with the command "apt-get autoremove", after your reboot.
If you want to use the new advantages of the kernel ( i.e. security fixes ), it is essential to reboot.