This page explains what Cauldron Cores are and how they work in Horizon Forbidden West.
Cauldron Cores are machine fabrication facilities run under the auspices of the Hephaestus AI, which has been manufacturing increasingly dangerous machines in response to humanity’s perceived threat to its more docile creations. Straying into the belly of the beast, is, understandably, a risky endeavor, as Cauldrons tend to be crawling with hostile machines.
Generally speaking, the goal of each Cauldron is to sneak, platform and/or fight through the dungeon until you reach the Cauldron Core, at which point you’ll need to override the core. Each Cauldron, its layout and its inhabitants are different, and as such the preferred means of getting through each one will vary, as well. Some require more puzzle-solving, some incentivize stealth, while others are more combat-heavy affairs. Once you enter, you often will not be able to escape a Cauldron via your means of ingress, so plan ahead before you commit.
In addition to the machines patrolling the exterior and interior of the Cauldron, the core itself is usually protected by a particularly nasty array of machines which must be dismantled before you can override the core in peace. For overriding a Cauldron Core you’ll typically get a quest reward, as well as an override code. This override code grants you the ability to override a variety of machines that share the corresponding code.