This is nothing to worry about, it has been a long time coming.
The current system of assigning IP addresses is known in the industry as IPv4 or Internet Protocol version 4.
Not sure how much people on here know about how the Internet actually works so if this isn't new information to some I apologise, but I hope some may find this interesting.
Every website address is what is known as a DNS address (The whys and what for arn't really important) however a plain text address means very little to a computer. www.google.com
for example must be looked up in the DNS table and mapped to an IP address which does mean something to the computer. There are different classes of IP address again the scope of the differences is of little importance, however if we quickly explore what an IP address is the significance of the depletion of IP addresses does become clear.
An IPv4 address is made up of 4 numbers separated by dots, for example 192.168.0.1, and on a class C IP address the first 3 numbers identifies what network a computer is on, and the last number identifies which computer on the said network this address relates to. People in the UK will recognise that this is similar to your post code, the first 2 letters and numbers relate to your area in the country, and the last 3/4 numbers relate to your specific house. Owing to the fact that any number in an IP address cannot be smaller than 0 or higher than 255 it does show that there are only a small amount of IP addresses when considering the number of computers and devises currently around the world.
As mentioned before this day when the last IPv4 addresses were issued has long been predicted, and luckily there is a new system in the waiting to take up where IPv4 ends, however strangely it is not IPv5! Instead it is IPv6 which is made up slightly differently to IPv4 addresses, again this is beyond the scope required to the casual internet user.
Whereas IPv4 only had 4294967296 addresses (Only!) IPv6 has approximately 3.4 times 10 to the power 38 addresses, or 340 with 38 zeros behind it! This should see us through for a couple more years. I did read somewhere that this means there are several billion IP addresses per square metre, covering the entire planet.
Hope that has been a little informative for you all. Any questions shout up!