This trick was originally described by @Arduino Enigma in the #Sinclair Scientific Calculator Emulator. Tented vias are vias that are covered with soldermask. If you think about it for a moment, there is really no reason for a via to be exposed (unless you re-use it as a test point). Its job is to connect the layers, and it does it as well when it is covered. On the other hand, when it's covered, the risk of shorting it is smaller, and the board can look much better.
Unfortunately Fritzing doesn't normally give you the option to have the vias tented. But there is a simple trick to add the soldermask over them when you are generating the gerbers. Start by generating your gerber files as usual, and once you do that, select Routing→Select All Vias from the menu, and press the Del key to delete them. It will also delete some of the traces, but don't worry about it. Now generate another set of gerber files, in a separate directory, and close Fritzing without saving the file.
Now all you have to do is to copy the maskTop, maskBottom, silkTop and silkBottom files from the latter directory to the former, and voila, your vias are now covered with soldermask. You can also only copy only some of those files to only have the vias covered on one side of the board.