Did an update for High Sierra. Now I can’t log on to my computer. Stuck in recovery mode.

Your computer's disk drive is in the process of being encrypted since that is the option you accepted when trying to install macOS. What you might try to do at this point is open Disk Utility and use it to erase your startup volume, usually named, "Macintosh HD" and indented under the main disk entry. I'm afraid you have no backup option. Follow these steps:

Install El Capitan or Later from Scratch

1. Select Disk Utility from the Utility Menu and click on Continue button.
2. When Disk Utility loads select the volume (indented entry, usually Macintosh HD) from the Device list.
3. Click on the Erase icon in Disk Utility's main window. A panel will drop down.
4. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
5. Click on the Apply button, then wait for the Done button to activate and click on it.
6. Quit Disk Utility and return to the Utility Menu.
7. Select Install OS X and click on the Continue button.

This will install the version of OS X you had installed.

The screen see is the Utility Menu of your Recovery HD. Whatever you had been doing has caused problems for your system. Based on what you have provided you need to erase the drive and reinstall macOS. If there is other information you simply chose not to post, then post it because we cannot figure out your problem or solution remotely. We lack such telepathic powers.