If you're not familiar with the problem, think about what happens when a state or city runs out of phone numbers and has to add a new area code. But what happens when we run out of area codes? Or what will happen when we run out of Social Security Numbers?
We have been talking about it for awhile.
There's this video from 4 or 5 years ago (long but funny).
And this video from just a couple years ago (long, not so funny, but informative).
It goes back further than that, but suffice it to say it's not taking anybody by surprise. It's now been a year since all the IPv4 address blocks ran out (No more IPv4 addresses, Internet Runs Out Of IP Addresses), although it will be awhile before individual addresses are all completely allocated. There are plenty of techniques to run multiple devices behind one IP address, and there may be some ways to recover some previously unused or unusable addresses. These workaround can cause as many problems as making the IPv6 jump might make, so it makes sense to get moving. As Randy Bush explains in the second video, those people and companies who get it figured out now will be leaps and bounds ahead of those who wait until crunch time.