The CAP theorem (also known as Brewer's theorem) of distributed systems says that you can have two out of these three:
Consistency means that you have the same state across all the machines in your cluster. Availability means that all the data is always accessible and partitioning means that the system can tolerate network partitions (some machines can't reach other machines in the cluster) without affecting the system's operation.
It's pretty clear that if there is a network partition and server A can't reach server B then any update to A can't be communicated to B until the network is repaired. That means that when a network partition happens the system can't remain consistent. If you're willing to sacrifice availability, then you can just reject all reads and clients will never discover the inconsistency between A and B. So, you can have C/P — a system that can remain consistent (from the user's point of view) and can tolerate network partitioning, but will sometimes be unavailable (in particular when there is a partition). This can be useful is certain situations, such as financial transactions where it is better to be unavailable than to break consistency.
If you can somehow guarantee that there will be no network partitions by employing massive networking redundancy, then you can have C/A. Every change will propagate to all servers and the system will always be available. It is very difficult to build such systems in practice, but it's very easy to design systems that rely on uninterrupted connectivity.
Finally, if you're willing to sacrifice perfect consistency, you can build A/P systems — always available and can tolerate network partitioning, but the data on different servers in the cluster might not always agree. This configuration is very common for some aspects of Web-based systems. The idea is that small temporary inconsistencies are fine and conflicts can be resolved later. For example, if you search Google for the same term from two different machines, in two different geographic locations, it is possible that you'll receive different results. Actually, if you run the same search twice (and clear your cache) you might get different results. But, this is not a problem for Google — or for its users. Google doesn't guarantee that there is a "true" answer to a search. It is very likely that the top results will be identical because it takes a lot of effort to change the rank. All the servers (or caching systems) constantly play catch up with the latest and greatest.
The same concept applies to something like the comments on a Facebook post. If you comment, then one of your friends may see it immediately and another friend may see it a little while later. There is no real-time requirement.
In general, distributed systems that are designed for eventual consistency typically still provision enough capacity and redundancy to be pretty consistent under normal operating conditions, but accept that 1% or 0.1% of actions/messages might be delayed.