The CAP theorem states that a distributed system can only provide two of the following three guarantees at the same time.

• Consistency (C): Every read receives the most recent write or an error.
• Availability (A): Every request receives a (non-error) response, without the guarantee that it contains the most recent write.
• Partition Tolerance (P): The system continues to operate despite an arbitrary number of messages being dropped (or delayed) by the network between nodes.

In a distributed system, network failures are inevitable. Therefore, a distributed system must choose between Consistency and Availability when a partition occurs.

• CP (Consistency + Partition Tolerance): If a partition occurs, the system stops accepting writes to ensure consistency. Use case: Banking systems, distributed locks (Etcd, ZooKeeper).
• AP (Availability + Partition Tolerance): If a partition occurs, nodes continue to accept writes, possibly leading to inconsistent data. Use case: Social media feeds, DynamoDB, Cassandra.
• CA (Consistency + Availability): This only exists in single-node systems or non-partitioned networks (which don't exist in the real world of distributed systems).

CAP is a useful mental model, but real-world systems often fall on a spectrum rather than being strictly one or the other. For a more nuanced view, see the PACELC Theorem.