What is CBIR & Basic IR?
The Competency Based Instrument Rating (CBIR) allows you to gain an IR in less hours than the "full" course, by either crediting previous experience or licenses.

I held a UK issued IR(R) (old IMC rating), which meant that I had approx 60 hours IFR time when starting my IR. A full IR would have meant 45 hours training, whereas the CBIR allowed me to do just 15 hours (in accordance with EASA Part FCL, Appendix 6). 

The BIR, as far as I am aware, is effectively going to mirror the UK IR(R) but make it a full EASA rating. That isn't confirmed however, as I haven't yet seen any official documentation from EASA.