Drop Edge Beams are the concrete around the edge of a concrete slab that hold the fill under the slab. Drop Edge Beams are usually used on slabs that require cut and fill to flatten the slope of the land. In simple terms, wood panels are used to provide the form work for the concrete to be poured to create the drop edge beams.
If you still don't quite get it, check out the diagram below of a Drop Edge Beam:
As extra wood form work is required and more concrete is needed to be poured, this is where the extra cost comes in. However, many builders will say that the price of the Drop Edge Beam is subject to the Contour Survey (which they will undertake after tenders have been signed). This allows the builder to hike up the price of the build once the site investigation and Contour Survey have been completed.
Make sure that you do not fall into this trap, so ask your builder upfront whether Drop Edge Beams are required, and if so, the costs involved.