Destroy the Core, or DTC is a gamemode which the goal is to leak the enemy's core(s). Most maps consist of 1 or 2 cores, and it is quite common to see maps with a mix of DTM and DTC. Cores will always lie symmetrically opposite of each other on either side of the map.
A core usually is an obsidian spheres with lava in the middle. In accordance with the map's XML, the core may change to different, easier to break blocks as time goes on. This helps the enemy team be able to leak the core, reducing the odds of the match becoming a stalemate. Once the obsidian core has been changed to another material, it will may be possible to leak the core using TNT. Therefore a common defence is to cover a core with water, which makes it impossible for the TNT to damage the core. As well makes it harder for the enemy team to move around and leak the core.