The orange color comes from insulation that covers the vehicle's liquid hydrogen and oxygen tanks. This is the same reason that the space shuttle's external fuel tank was orange. The first two shuttle flights, STS-1 and STS-2, in 1981, featured tanks painted white to protect the shuttle from ultraviolet light while sitting on the launch pad. But after engineers concluded the protection was unnecessary, the white paint was discarded, freeing up 600 pounds of weight in the process.
Ares V, NASA's original heavy lift vehicle proposed for the post-shuttle era, also would have had brown insulation covering its core stage. At a glance, SLS now looks quite similar to Ares:
The Constellation program—and thus, Ares—was axed. When NASA debuted SLS in 2011, the 8.4-meter-diameter core stage had a pearl-white paint job and Saturn V-style livery, invoking nostalgia for the time when mammoth rockets carried astronauts beyond low-Earth orbit.
The Space Launch System (original concept)
Many internal NASA documents, however, used SLS artist's concepts with orange core stages. Over the past year, I've raised the paint job question with several NASA engineers and managers, and received conflicting answers. It became clear that the shiny white SLS renderings NASA was using might not match reality.
As if to placate anyone disappointed over the switch from white to brown, the new SLS renderings include orange and grey swirls on the aft ends of the solid rocket boosters. This immediately made me think of ATK's Liberty rocket, and the Ares I-X booster. Orbital ATK manufactures the Space Launch System's five-segment solid rocket boosters.