My BeagleBone came with Debian 7 installed. To update it I accomplished the following steps:

1. Head over to https://beagleboard.org/latest-images and get the latest image
2. On macOS, install xz, unpack the ter.xz file and flash the SD card you want to use:

brew install xz
xz -d bone-debian-8.7-lxqt-4gb-armhf-2017-03-19-4gb.img.xz

#find the device name of the SD card
diskutiel -l
#in my case it was /dev/disk2; CHECK THIS FOR YOUR SYSTEM!
#umount the disk
diskutil umountDisk /dev/disk2
#flash the image. This took about 20 minutes on my computer
sudo dd bs=1m if="bone-debian-8.7-lxqt-4gb-armhf-2017-03-19-4gb.img" of=/dev/disk2

3. Eject the SD card and remove it from your PC. Make sure to power down your BeagleBone and remove all connections (power, ethernet, wires, etc)
4. Insert the micro SD card into the BeagleBone and apply power. It will boot from the SD card, wait for the boot process to finish
5. After SSH’ing into the BeagleBone uncomment the following line in /boot/uEnv.txt

sudo vim /boot/uEnv.txt
---------------------------------------------------------
##enable Generic eMMC Flasher:
##make sure, these tools are installed: dosfstools rsync
cmdline=init=/opt/scripts/tools/eMMC/init-eMMC-flasher-v3.sh

 

6. Shutdown the BeagleBone and remove the power cable. Before you plug in the power cabe press and hold the boot button (the one near the SD card slot). After plugging it in, wait for the led’s to flash. As soon as you let go the button the led’s should flash in a rhythmic pattern (from left to right and then from right to left and so on).

When the image is written to the eMMC all four led’s will be lit and the BeagleBone will shut down. As soon as all led’s turned off you can remove the SD card. When you boot the next time (without the SD card) you can check if everything worked with

lsb_release -a