When talking about distributed systems, it is common to describe Eric Brewer's CAP Theorem as "Consistency, Availability, and Partition Tolerance. Pick Two." This is usually illustrated with a triangle or Venn Diagram. While that's not terribly wrong, it's not particularly helpful.
Given that network partitions are rare, but do happen, the better way to consider the theorem is: "In the event of a network partition, does your system guarantee consistency or availability?"
Lets say you have a system with incoming data.
If your system splits, do you stop accepting data (choosing consistency, sacrificing availability), or do you accept the requests and attempt to "fix" the integrity of the data at a later point (choosing availability and living with "eventual consistency")? Even from this simplified diagram, it is clear that is absolutely impossible to have a full system with all three properties at the same instant, which is why the CAP theorem is provably true.
I have found this illustration somewhat more helpful and somewhat more correct than triangles. The theorem is certainly quite nuanced, and I plan to write on other aspects of the theorem and distributed systems in the future.
I definitely want to give a hat tip to Nathan Marz
for a similar explanation which I repurposed here.