The CAP theorem, also known as Brewer’s theorem, is a fundamental principle in distributed systems formulated by Eric Brewer. It states that a distributed system can achieve only two out of the following three guarantees simultaneously:

1. **Consistency (C)**: Every read receives the most recent write or an error.
2. **Availability (A)**: Every request receives a response (success or failure), without guarantee that it contains the most recent write.
3. **Partition Tolerance (P)**: The system continues to operate despite network partitions, where communication between some nodes is lost.

The importance of the CAP theorem lies in its implications for designing distributed systems. It highlights the trade-offs that system architects must make:

– **CA (Consistency and Availability)**: Sacrifices partition tolerance. Suitable for systems where network partitions are rare.
– **CP (Consistency and Partition Tolerance)**: Sacrifices availability. Used in systems where data consistency is critical, even if it means some data might not be accessible during partitions.
– **AP (Availability and Partition Tolerance)**: Sacrifices consistency. Suitable for systems needing high availability and fault tolerance, like many web services.

Understanding the CAP theorem helps developers make informed decisions about system design based on their specific requirements and constraints, balancing trade-offs to meet desired system behavior.