This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
It had the unfortunate distinction of being ground zero for the Burn in 3069. Ironically, when it was re-discovered a century later, its abundance of dilithium was crucial in allowing the United Federation of Planets to recover.
Theta Zeta's environment was extremely harsh, bombarded by lethal radiation consisting of two types of theta radiation, delta radiation, electromagnetic radiation, subspace radiation, and two hitherto unknown forms of radiation.
Its surface was marked by massive concavities and it was orbited by chains of numerous small asteroidal bodies. It had large quantities of dilithium and was identified with a dilithium nursery. (DIS: "Su'Kal")
In 3064, the KSF Khi'eth, a Kelpien research vessel, crashed on Theta Zeta while investigating the dilithium nursery. Five years later, Su'Kal, a child born to Dr. Issa among the wreckage, witnessed the death of his mother by radiation poisoning and screamed in horror. Because his genes had mutated to interact with dilithium in unique ways, and dilithium had a subspace component, this scream unleashed the Burn across the galaxy without his knowledge. (DIS: "Terra Firma, Part 1", "Su'Kal", "That Hope Is You, Part 2")
In 3189, the Federation starship USS Discovery tracked the source of the Burn to Theta Zeta. Cleveland Booker was able to identify a pocket within the Verubin Nebula near the planet for Discovery to spore-jump to in an attempt to investigate the crash site of the Khi'eth, apparently the only structure on the planet/planetoid. When Captain Saru, Commander Michael Burnham, and Doctor Hugh Culber transported to the ship, they found the sole life sign to be Su'Kal, still alive and living in a holographic simulation. Saru, Culber, and Adira Tal stayed behind on the Khi'eth to attempt to reach Su'Kal while Burnham returned to Discovery with Booker to retake the starship from Osyraa and the Emerald Chain. (DIS: "Su'Kal")
Osyraa, eager to mine dilithium from Theta Zeta, tried to torture the planet's location within the nebula out of Booker, but Burnham rescued him before she could break him. After Discovery was re-taken, the vessel jumped back to Theta Zeta and rescued the away team and Su'Kal moments before the Khi'eth's remains finally fell apart.
This planet's name was only mentioned in writing. It was described there as a "planet/planetoid", although in dialogue it was consistently referred to as a planet. Digital artist Timothy Peel referred to Theta Zeta as "the dilithium planet," noting on Twitter that it was "a complex planet to render and animate!" 
In "Su'Kal", Owosekun says that the Khi'eth crash site on Theta Zeta is located "two hundred kilometers into the nebula." Given the apparent size of the Verubin Nebula – large enough to make locating the planet difficult for Osyraa in "There Is A Tide..." – this comment should perhaps not be taken at face value.