Last week Apple released a minor patch for OS X in the form of a kernel extension update. Labeled "031-51913 Incompatible Kernel Extension Configuration Data 3.28.1," the update turned out to be bugged, leaving many Mac users without a working ethernet port. Well, at least those with Macs that still have ethernet ports. It took a little time, but Apple has acknowledged the bug offered a solution for those affected.
First off, if haven't already downloaded and installed the update, there's no need to worry. Apple pulled the update, fixed the bug, and has released a new version. So if your Mac is showing that you need the kernel extension update, go ahead and grab it. On the other hand, if you installed the patch and your ethernet port doesn't work, Apple's Support site has you covered.
First thing to do is check which version of the Incompatible Kernel Extension Configuration file is installed. You can do this by opening the System Information app: either hold down the Option key and click the Apple menu on the far left of the menu bar, or just "System Information" into Spotlight search and it will be the top result.
Once System Information is open, navigate to Software in the left-side menu, and under that Installations. The list on the right side is alphabetically sorted, so look for the row labeled "Incompatible Kernel Extension Configuration Data" and check the most recent version number. If it says 3.28.1, you'll need to update the profile.
If you can connect to a WiFi network you can take the easy route; open Terminal (type "terminal" into Spotlight), then enter this command, after which it will ask for your admin password:
sudo softwareupdate --background
Then just quit Terminal and reboot the Mac, and after startup the ethernet port should work again.
If you can't access WiFi, you'll have a bit more work to do. The steps are long in number, but Apple's Support site breaks it all down and offers a detailed explanation. Basically, it involves restarting in Recovery mode and manually deleting a few files through Disk Utility and Terminal. The last step will be to enter the above command from the WiFi method and reboot.