A reef band is used in situations where it is necessary to secure the interior of your tarp. For example, suppose you are hanging a large tarp from your ceiling. If you only secure this tarp on the outer edges, it would tend to droop down in the center. To prevent this, you would need to add grommets to the interior of the tarp. If we just put grommets into the middle of the tarp (without a reef band), to use these to secure the tarp you would need to run your rope into one grommet and then out an adjacent grommet (to return the rope to the side of the tarp on which it went in). When we use a reef band, your rope can be run in and out of the same grommet.
A common application for a reef band is when covering tall fencing. Suppose you have an 8-foot fence and you just secure your tarp to the top and bottom. In this case, the wind would cause the tarp to billow out in the middle. To prevent this, we can run a reef band along the middle of the tarp (at the 4-ft point) from one end to the other so that you can secure the tarp to the fencing along the top and bottom as well as horizontally along the middle.
Note that covering fencing with solid tarp material is very risky and generally not recommended since the added wind force could cause the fence to blow over.