"Supports" are akin to temporary beams used to hold a beam up in place as you build the rest of a building, they let the molten plastic set before it sags etc.
On some dual head printers (where you can print with more than one type of filament) they use PVA (Polyvinyl Alcohol) as a support, then once the print is done, warm to hot water will dissolve the PVA and your supports are gone with no marks. More complex than printing everything in one filament though.