During Apple's recent iPad announcement CEO Tim Cook made several references to the "post-PC era". This led to a flurry of articles on the topic.
At the simplest level, the post-PC era refers to the growth of computing devices that are not traditional PCs. More specifically, the current use of the term refers to the growth of smartphones and tablets.
The term and concepts date back at least to the late 1990s when discussions of computer and Internet enabling wristwatches, glasses and other objects were quite popular.
The chart below, from Business Insider's article on Apple's iPad announcement, does a nice of job summing up the reasons why people are again talking about the post PC era. The chart shows the number of devices shipped in Q4 2011 by the major PC manufacturers compared to iPad shipments.
As you can see, Apple sold more iPads than any of the major PC manufacturers sold PCs. Apple also sold 172 million post-PC devices last year (defined by Apple as iPods, iPhones and iPads).
So the post-Pc era is clearly here, but that doesn't mean traditional PCs will go away any time soon. Most forecasters are suggesting the market for traditional PCs (desktops and laptops) will continue to grow over at least the next 3-5.
Instead it means a proliferation of the types and numbers of computing devices we use. For example, when I travel I carry 3 computing devices, 2 of which are post-PC - an iPhone, a MacBook Air and an Amazon Kindle Fire. Each plays a role and adds to my productivity.