A planetary core or simply core was the innermost layer at the center of a planet or an asteroid, in the same way that a stellar core was the center of a star.
The core was divided into an outer core and an inner core. (TNG: "Inheritance")
M-class planets had a nickel-iron core. (TNG: "Clues")
In 2258 of the alternate reality, Nero used a mining drill on the Narada to dig to the core of Vulcan. He then put red matter into the core of Vulcan, creating a black hole and destroying the planet. (Star Trek)
The planet Terra 10 had a molten core surrounded by a mantle and crust that were entirely crystalline. (TAS: "The Terratin Incident")
In 2285, Hikaru Sulu reported that Genesis' core was unstable. (Star Trek III: The Search for Spock)
The gas giant Tethys III had a frozen helium core. (TNG: "Clues")
In 2368, an asteroid which threatened Tessen III with planetwide destruction had a core of nitrium and chrondite. (TNG: "Cost Of Living")
The moon Jeraddo around Bajor had a molten core, and in 2369, there were plans to transfer energy from this core, forcing the evacuation of the residents. (DS9: "Progress")