Cap Theorem is a theory about how to decide which parts of a database system are the most important. It says that when designing a database system, you can have only two of three things: Consistency, Availability, and Partition Tolerance.
Consistency means that if you read something from the database, you can trust that it is the same everywhere.
Availability means that when you try and read or write something to the database, it will always work.
Partition Tolerance means that the database system can keep working even when parts of it are not connected.
Cap Theorem says that you can only have two of these three things. So if you want data to always be consistent and always work, you'll have to give up some of the partition tolerance; but if you want it to always be available, you'll have to sacrifice some data consistency.