Vase mode is an incredible feature for making really nice 3D prints. I'm a big fan of printing out vases, since they look really good, are functional, don't use a lot of material and are great for giving away to people who don't have 3D printers.
To enable vase mode, click "Edit Process Settings", then go to the Layer tab and enable the option for Single outline corkscrew printing mode.
Single outline corkscrew printing mode (vase mode): The extruder will print with one outline/perimeter shell and won't make any retracts. This means that it will slowly move up in the Z as it prints, imagine spiraling upwards, instead of printing a static layer, than moving upwards to do another layer. This means there shouldn't be any seams in your print or any spots where retractions occurred, meaning that the prints come out extremely smooth.
With vases the best settings I've found are Zero top solid layers, 3 Bottom Solid Layers, and under the Advanced tab enable "Merge all outlines into a single solid model".
Also, under the extruder tab, you change your extrusion width slightly if you want to adjust the thickness of the walls of the vase. For instance, if you have a .4 mm nozzle, but want a thicker vase, you could change the Extrusion Width to .50 mm.
Overall though, Vase model is for much more than just vases. Really any part that has a single "island" that can be printed without support and 0% infill is a good candidate for vase mode, since it will produce extremely clean perimeter outlines with no retractions. For instance, if printing a model of a pyramid, you could definitely use Vase-mode and get a really nice finish!
Also, to expand on the setting for "Merge all outlines into a single solid model" - This feature in the software will slice the model taking all of the outer most perimeter outlines. For instance, if you had a model that was a block with screw-holes in it, but had "Merge all outlines into a single solid model" on, the holes would not show up. Using Merge all outlines is generally really useful for models that have errors in the mesh or if using Vase Mode.
Lastly, vase mode will work for parts that do have multiple island - a great example is this part (http://www.thingiverse.com/thing:323038
). It transitions from multiple island (2) at the lower half with the tail and body, but then to a single island at the top. You might look at it and say because there will need to be retractions between these islands that vase mode wouldn't work, because the tail would be an island and the body would be an island. But the software will actually intelligently switch back and forth between normal printing mode and vase mode if you try to slice that model using vase mode settings. This means that even if a model has areas with multiple islands, that aren't compatible with vase mode, you can still use that settings, and the software will automatically choose the best method as it goes.
The part only has retractions where multiple islands are, where retractions are needed!