The ability to change the size of a block is a removed feature. It never was in the public version of the game, and was supposed to be in the 2.0 Update. They were too hard to program so they got cut in order to get the update out faster. This feature would have given the user the ability to change the three dimensional size of any block in the game. The normal block size is 1x1x1, so the small block is 1/2 that size (eight small blocks stacked in a cube is equal to one normal sized block), and the the large block is 2x2x2, or 2 times the size of a normal block (eight normal blocks stacked together in a cube is equal to one large block).
Half-blocks were blocks that had a dimension of 2x2x1, meaning that they have the same dimensions of a normal block, except their height is half as large (four small blocks are stacked in a square is equal to one half block.