Large cardinals are such cardinals whose existence cannot be proved within $\sf ZFC$, and requires stronger axioms to be added to $\sf ZFC$, they are often used to measure the consistency strength of a certain statement in the language of set theory.
For further reading:
- Kanamori, Akihiro. The Higher Infinite : Large Cardinals in Set Theory from Their Beginnings
- Kanamori, Akihiro; Magidor, M., The evolution of large cardinal axioms in set theory