It will take a minute or two to extract the file, and you should then end up with a 3.66 GB .img file (notice that the .xz is removed from the file extension).
There are now a few ways to continue. You can use terminal commands, or software that will guide you through it. Let's start with the guided software using a graphical interface.
Using a GUI
First, you'll want to download PiFiller. It was designed to install images onto SD cards for the Raspberry PI, but there isn't any reason why it wouldn't work for BeagleBone images as well.
Once you've downloaded Pi Filler, locate it in Finder (typically Downloads), and double click it to extract it. You may want to copy it to your Applications folder.
Then, insert your microSD card into your Mac, and click Continue. Pi Filler will look for your SD Card, and then notify you once it finds it.
Navigate to the Flashing the BeagleBone Black page, and follow the instructions on how to flash the newly copied image onto the on-board flash memory of the BeagleBone Black.
Using the command line
Another alternative is to flash the microSD card entirely from the command line. You'll first want to extract the img.xz file you've downloaded, and the best program for that is still "The Unarchiver" mentioned in the GUI instructions. Once you've got the extracted .img file, open a terminal to get started.
Execute the following command to see the list of connected storage devices:
df -h
df -h
Once you've got the name of the device, you'll want to unmount that disk using the following command, but replacing the specifics with your card details:
sudo diskutil unmount /dev/disk4s1
Note that we subtly changed the device name from "/dev/disk4s1" to "/dev/rdisk4". You'll want to do the same when you execute the below command.
Also, choose the right file location for your .img file in the input file field (if=...).
sudo dd bs=1m if=~/Downloads/BBB-eMMC-flasher-2013.05.08.img of=/dev/rdisk4
Navigate to the Flashing the BeagleBone Black page, and follow the instructions on how to flash the newly copied image onto the on-board flash memory of the BeagleBone Black.