Machine Bases are similar to Machine Frames in that they are a crafting material, however the resulting machines are slightly different.
Machine Bases produce machines that are a quarter of a block high, and usually have some form of redstone output or input.
When you place one of these machines, the direction it faces is determined by which edge of the block your cursor is closest to.
It may help to imagine an X on the side of the block you are placing the machine on, then think about which 'quarter' of the X you're looking at.
The output will be facing this direction and the input will come from the opposite direction.
This is particularly useful for placing these machines in cramped spaces or on walls - which is one of the more convenient features of these blocks.
Of course, if you don't like the direction the block is facing in, you can always Wrench it - just right-click with the wrench in Wrench Mode to change the direction it's facing in.
The Machine Base does nothing on its own, but is used in many recipes as the base for other blocks.