A vertical worm bin or a stacked bin worm farm consists of a number of bins which stack one on top of the other.
The reason a vertical worm bin system works is that the worms that are used for worm farming, Eisenia Fetida, are top living worms. They like to live at the top surface of a worm farm which is where the food is.
Like a simple worm bin the worms are established in one of the worm bins, once this bin is full an empty bin is placed on top of it so that the bottom of the empty bin touches the castings underneath. The bottom of the empty bin has a number of holes in it which the worms use to move through to the bin above.
Once the top bin is full the bottom bin can be harvested as most of the worms will now be living in the top bin. If the top bin fills up too quickly with castings there may still be worms left in the bottom, in this case an additional empty bin can be placed on top (as in the picture). This will give the worms at the bottom adequate time to migrate to the surface.
The majority of small worm farms are of a vertical design. This is because they are probably the best suited to small scale worm farming and are convenient to use.
Using more than two or three bins does not give any real advantage. The worms will regulate their population based on the surface area of the farm, not on the volume. Adding extra bins will not result in a large increase in worm population. If you want more worms rather use bigger bins.