In a nutshell, the new version of the API removes the ability to track what others are doing to your avatar. You'll still see various effects, but you'll no longer see which spell was cast. The impetus behind the changes seems to be to level the playing field between those using the standard UI and those using add-ons like Foundry Tactical Combat.
[Update: Tipster Vinicius let us know that the ESO team has also posted a fresh Ask Me Anything on Reddit. The devs discuss beta wipes, load capacity, bug fixes, and more.]