FHIR (pronounced 'fire') builds on the HL7 v.3. It's been introduced at the end of 2011 and has been implemented to improve interoperability (exchange of data) between health units. The need to exchange healthcare information electronically has been around for over decades - HL7 v. 2 is 25 years old!
Currently FHIR is only a DSTU (Draft Standard for Trial Use) which means everything can change. However, the good thing is that this is an open standard and you can freely use it without any restriction (but also without any guarantee).
FHIR is gaining so much popularity because it addresses several issues which are either not present in the current standards or it's a pain in the bottom to implement or you cheat the implementation and make it interoperable.
FHIR broadens the scope of sharing healthcare information across organizations and different disciplines. It also address the issue of mobile devices and cloud-based applications for stability. Most importantly however, it can be implemented really fast; integration can happen in days/weeks rather than months and this is what makes is so attractive.
There are various server implementations already available: most notably Happi (based on Java). The acronym FHIR stands for: F - Fast (to design & implement), H - Health, I - Interoperable, R - Resource.