Steven Cheung, Vidabox President, does a good job explaining the differences between the various versions of HDMI.  We are reposting excerpts of it here for your benefit:

In short, the differences are in the feature available and which
audio-video formats can be transmitted through that connection.  To
start - practically ALL AV devices manufactured today (DVD players,
set-top boxes, VidaBox media systems, etc.) have HDMI1.2 as the minimum standard, providing audio + video on one cable.  Here's what the newer standards provide.

HDMI1.3 adds support for the 7.1 lossless HD audio formats, such as Dolby TrueHD, DTS-HD, and DTS-MA (Master Audio).  This is of particular importance for Blu-ray since this is the minimum requirement to be able to enjoy to these new audio formats in a home theater.  When a client is asking for the best audio quality possible, make sure your setup (source & receiver) has HDMI1.3.

Another feature that HDMI1.3 adds is "Deep Color" - but at the time of this writing, there are still no sources for "Deep Color."  So, if a customer asks about this, it's a somewhat moot point as there are no commercially-made Blu-ray titles taking advantage of this feature.

HDMI1.4 adds support for native 3D over HDMI, assuring a "plug-n-play" 3D experience.  It also provides support for 4k x 2k resolution support, which appeals to digital signage and large multi-display installations.

Other features added with 1.4 is an Ethernet and audio return channel, but in most multizone AV installations, there are other (easier) methods of carrying this out, and avoid the headaches that HDMI generally brings to installations.