Support structures: Support structures are temporary material printed under overhangs and bridges so a 3D printed part can be built, then removed after printing.
A printer cannot lay material on thin air. FDM and resin printers add supports under faces that lean past the critical overhang angle; metal powder bed machines add them to anchor the part and draw heat away. Polymer powder bed processes such as SLS and MJF need none, because the loose powder holds the part.
What it means for the price
Supports cost three times over: the material they use, the machine time to build them, and the labour to remove them and clean up the marks. Support removal on resin and metal parts is especially slow work. Orientation changes support volume, so the same part can be cheap or expensive depending on how it sits on the bed. A quote that ignores support volume underprices awkward parts.
Example: a part that needs 8 g of support for 30 g of model adds about a quarter to its material, plus some minutes of cleanup. The figures are an example.
Common confusions
Breakaway supports and soluble supports are different things. Soluble supports, PVA for example, dissolve in water instead of being snapped off; they leave cleaner surfaces but cost more and print slower. Support cleanup is one part of post-processing. Read design for 3D printing for ways to need fewer supports.
Go deeper: Design for 3D printing: walls, overhangs, holes, clearances and orientation