Curses are abstract concepts tied to barely tangible symbols that represent a specific kind of absolute power. Notable curses are the aspects of Homestuck, the symbols on Bill Cipher's Zodiac, and the symbols of the Order. Curses have specific effects that they grant to their user, and can only be destroyed through suitably abstract means - but even the destruction of a Curse is very rare.
Godmodders have the power to use Curses at any time during battle. They only last for a specific timeframe, but higher-level godmodders can keep them going for months or years; a long time in terms of a battle. In the terms of a godmodder, Curses project negative effects onto the battlefield that affect the Anti-Godmodders and their entities. Typical examples used throughout the Destroy the Godmodder series are the Curse of Repetitiveness, Curse of Entities, and Curse of Charging.
The Curse of Repetitiveness, arguably the most common Curse, makes it so an attack will never work more than once against a godmodder and that the more a certain attack, item, or entity is used, the weaker it will get. Pro-Godmodders are affected by this to a negligible extent, but the entities the godmodder summons aren't. In fact, they will get stronger with each summon.