Vacuum-jacketed distilling column
The purpose of the vacuum jacket is to provide insulation of the column from cooling by ambient lab air.  You don't want to have to heat the "pot" (the flask containing the crude material you want to purify) any more than you have to, otherwise heat sensitive material in the pot may degrade and turn to tar.  Imagine if you cooled the exterior of your distillation column with cold water while performing the distillation.  You'd have to heat the pot a LOT more to get the material in the pot to finally reach the top of the column, then if you weren't cooling the column.  Air will have the same effect on your distillation, albeit to a smaller extent, than cold water.  So to avoid putting unnecessary extra heat into the pot, you vacuum jacket your column to preclude undesired cooling by ambient air.  

Remember, a distillation column is different than a condensing column.  You don't want to cool a distillation column, you do want to cool a condensing column (or condenser).  Back in the day, very long columns were sometimes needed in the organic lab (5-10 feet) to separate closely boiling materials, they are still used in industrial applications.  If you had a 10-foot column that wasn't vacuum jacketed, you would turn most of your material to tar before it distilled over, because of the extra heat you had to supply to make up for the undesired cooling of the column by ambient air.  Eventually improvements like column packing materials (glass beads for example) and spinning bands (a metal helix rotating in the column) came along to increase column efficiency and allow chemists to be able to get good separation efficiencies (measured as "height equivalent theoretical plates", HETP) without having to resort to long columns.  Still a vacuum jacketed column is preferred to lessen unnecessary heating.