First, the things you know about:
Biomes
This should be pretty obvious as soon as you look at the home page. The traditional "grab eggs from the cave" has been replaced with a map guiding you to six biomes. Each biome has an exclusive set of breeds to choose from. Note: The AP is still accessible from the home page, and there is currently no "blocking" mechanism in place.

Egg/Hatchling Limits
This update is double the awesome. Not only is the somewhat-convoluted egg/hatchling limit linkage thing gone (No more 4 hatchlings and 2 eggs being "locked"), but the limits are also increased based on your trophy level. New users can have 4 eggs with 12 total growing creatures. Bronze badge brings you up to 5 eggs/15 total, silver is 6/18, and gold is a whopping 7 eggs at a time with 21 total living things. More on how this works will be added to the help page soon, but hopefully it's much easier to understand than the old system.

Purple BSA: Fertility
Use this BSA to increase the chance of a successful breeding. Just choose one dragon to use it on, and the next time they breed their chances will be upped. Using it on both dragons on a pair does not produce any increased effect.

Magi BSA: Teleport
Transfer or trade your dragons. This long-awaited feature is now finally available, bringing an official trade feature to DC.

Rare x Rare Breeding
The limitation preventing you from breeding rare dragons (or Frill x rare, etc) together is now gone. However, the chance of successfully producing a rare from rare x rare is about the same as breeding common x rare, except you use two rares in the process, so choose wisely.

Rejections in Breeding Lists
Dragons that have rejected in the past should no longer show up in the breeding list. I am aware that there will probably be false positives (Rare x rare pairs bred before today). Don't worry, I'll be doing something about this soon.

And the things you weren't expecting:
Updated Navigation
Also pretty noticeable as soon as you visit. I made the navigation smaller to make room for an increased number of links, including a help link.

Help Page
The help page, previously hidden away, has been fleshed out. The introduction has been clarified, a page on "the ratios" have been added, and the new BSA's are listed as well.

Account/Dragons Split
There've been a lot of "account management" links shoved on the top of the "view dragons" page for a while. It made a lot of sense to separate the two into distinct pages. Note that you can also easily access your active trades and transfers from the account page.

Five-letter Codes
To make room "for the future," all new dragons now have five-character ID codes instead of four. This certainly makes a lot of room for funny new words. Existing dragons are completely unaffected.

Codes in breeding list
When breeding, the "Unnamed" text has been replaced with the dragon's ID. This should make it easier to tell what dragon you're choosing for breeding.

Layout switching
If you go to "Account Settings," you'll find the option to change the site skin. Tired of the boring paper? Switch to the Portal 2-themed layout. Remember the 2009 St. Patrick's Day skin (Of course not, only five people got to see it due to host issues/lag)? Well now you can use it all the time.