Artificial suns were artificially maintained stars. They gave off artificial sunlight.
The Martian Terraforming Project had intended to heat Mars with several artificial suns around its orbit once Mars was terraformed. This fell through when the Great Recession forced the project to be abandoned. (AUDIO: Deimos)
In the 23rd century, the Eighth Doctor caused an explosive feedback in the still intact atmospheric re-ioniser of the abandoned Martian project, causing both — according to one account — the terraforming of Mars and the ignition of Deimos Moonbase's atmosphere once the re-ioniser exploded. This chain of events turned Mars' moon, Deimos, into an artificial sun that could heat Mars' atmosphere. (AUDIO: The Resurrection of Mars)
The Aapex Corporation created artificial suns for Nooma which also functioned as starships. By the time the Third Doctor visited the planet, only one of them was still functioning. Juliu Epreto wanted to take control of it and use it to depart his world, but the Doctor prevented him from doing so. (PROSE: Speed of Flight)