Answer My Own Question:
Consistency model is too formal and rigorous to explain to general audience. Fortunately (or maybe unfortunately), most people have the experience of data inconsistency. Data inconsistency often means strange behaviors to users. Basically, consistency models specify what behaviors are allowed and what are not. The key point here is there are various consistency models of different levels. The stronger the consistency model is, the less surprises the user gets. Strong consistency is desired for both users and developers: Users feel better about their data and developers find it easier to program.
Typical consistency conditions include (but are not limited to) eventual consistency, causal consistency, sequential consistency, and atomicity, from weak to strong.
Eventual consistency is prevalent in today's distributed storage systems, represented by Amazon's Dynamo. Eventual consistency is quite weak (in theory) because it makes little promises. Consider the following scenario (shown in figure):
data-inconsistency-eventual-blog http://i1.tietuku.com/48f5bfa9d6d925e0s.png
You have just finished your blog and can't wait to publish it. You push the "publish" button and immediately refresh the page and only to find that your blog is not there! It does happen when you publish your blog to a replica node and refresh on another one. Take it easy. Refresh, refresh, refresh, and it will appear eventually.
Causal consistency is stronger than eventual consistency in that it guarantees that two causally related events are observed by all the users in the causal order. Consider the following coined conversation on a social networking site (shown in figure), excerpted from a paper:

- The mother cannot find her son and posts a status to her friends: "I think Son is missing!".
- The son replies to his mother to let her know that he is just playing out.
- A friend observes this little conversation and posts a status in response: "What a luck!".
If causality is not respected, a third user could perceive effects before their causes. As shown in the right figure, she might think the friend is pleased to hear of the Son's disappearance!
Mission critical applications usually require much more stronger data consistency, such as transaction.
[To Be Continued]