Software written using SFML 2 would need its SFML parts to be modified to match the version 3 interface.
Breaking, in this context, basically means that existing version 2 programs won't run as is without modification.
Note that this is identical to the 'breaking' interface of SFML version 2 from version 1.
It allows major updates to SFML without requiring direct backwards-compatibility. For example, SFML 3 will use C++11 (or later) whereas SFML 2 does not so C++11 (or later) compiler will be required for SFML 3.
All this helps us to understand that it might be some time before SFML 3 appears.
I'd like to know the current design for 3's interface is shaping up (if it's begun) so we can be prepared for it.