The CAP theorem, formulated by Eric Brewer, states that in distributed systems, it is impossible to achieve consistency, availability, and partition tolerance simultaneously, forcing designers to prioritize two out of the three. Misunderstanding the theorem can lead to poor design choices, especially as the future direction of databases leans heavily towards distributed architectures. Additionally, the document explores eventual consistency, real-world examples like Dropbox, and issues related to split-brain syndrome in distributed systems.