The Honey Jarring Machine can be crafted at an Apiary Crafting Station. To use it, place Empty Bottles and any of the various Honeycomb in the input slots. It will extract the honey into bottles and put it in the output slots.
The Honey Jarring Machine used to require the Industrial Centrifuge to work. This would allow extracting both bottled honey and the items the centrifuge would produce. However, as of 5.6.259 (commit 45a33969), the machine no longer requires or uses the Industrial centrifuge, requiring the player to choose between bottled honey or centrifuged items. This was done by shifting the script used for the machine from honeyjar.lua to a new honeyjarrer.lua script. This change was intentional (see the creator reply in this Reddit thread). The model for the jarring machine was not changed and still looks like it connects to the Industrial Centrifuge when placed next to it.