Krios Prime was the main planet in the Kriosian system. This system was near Starbase 117 and was the homeworld of the Kriosians. Krios or Krios Prime was named after Krios, who ruled the ancient Kriosian Empire with his brother Valt. The brothers became divided over the love for a woman named Garuth so eventually their empire fell. Krios even kidnapped Garuth from her homeworld Valt Minor and took her to Krios Prime, which started a centuries-long war between the two worlds. (TNG: "The Perfect Mate")
By the 22nd century, the Kriosians were under the rule of the Sovereign Dynasty of Krios Prime, a family known on hundreds of worlds. The royal guardsmen of the Dynasty were known as the Sovereign Guard. Their leader was known as the First Monarch, a post which Kaitaama would ascend to in 2153. (ENT: "Precious Cargo")
By the mid-24th century, the Klingons had established colonies on Krios and suspended Kriosian sovereignty. In 2367, the Federation was accused by the planet's governor, Vagh, of aiding the planet's rebels who hoped to free the planet from Klingon rule. However, with the help of Klingon Ambassador Kell, it was revealed that the Romulans were secretly aiding the rebels. (TNG: "The Mind's Eye")
In 2368, Krios and Valt Minor took their first steps towards ending an ongoing war as Kamala, the first female metamorph born on Krios since the mid-23rd century was delivered for marriage to Chancellor Alrik of Valt Minor. (TNG: "The Perfect Mate")
There is debate about whether the planet seen in TNG: "The Perfect Mate" and referenced in ENT: "Precious Cargo" was the same planet seen in TNG: "The Mind's Eye". There was no definitive statement in any episode to clarify their status. The name used in TNG: "The Mind's Eye" was the same as in TNG: "The Perfect Mate" but no other similarities exist. The planet's color changed between episodes which could indicate an unintentional production mistake or an intentional differentiation between two different planets (see images).
In ENT: "Precious Cargo" the matter was further complicated in a conversation between Trip and Kaitaama. As they part ways, it was made clear that there was more than one planet with the name Krios. Trip asks to simply visit Krios causing Kaitaama to correct him by saying "Krios Prime." The inclusion of this trivia by the writers was unnecessary for advancing the plot but was very useful in discerning that there was more than one planet with this name.
According to the Star Trek: Star Charts (pg. 63), the Kriosian system was located in or near Klingon space, in the Beta Quadrant. This system was a single star system. Primary was a Class G star with a magnitude of +5, which was the same brightness as Sol.