What is the major technological change that has dramatically improved GPS acquire time?
As with most things, there are several things that have made acquisition time faster:


The very first GPS's could only receive a signal from one satellite at a time.  It would have to switch quickly between satellites to make it seem like it was doing more.  Modern GPS's can receive 12 to 24 satellites at a time.
Decoding a GPS signal is computationally complex.  Modern GPS receivers have more "decode units" (sorry, I forgot the official name for them), allowing them to lock onto the signal quicker.
Modern GPS receivers are more sensitive and can receive weaker signals.
Some GPS receivers have a barometric altimeter, which normally helps the GPS get a more accurate position fix when not many satellites are visible-- but also helps get the initial fix quicker.


That being said, there are some things that smartphones do that normal GPS receivers cannot.  I suspect that this is the true reason for the new Android phones quick fix, and for getting a fix indoors.

Smartphones use three different types of positioning methods:  GPS, Cell Tower triangulation, and WiFi.  With cell tower triangulation it basically detects the signal strength to/from several cell towers and triangulates from that.  WiFi positioning is basically detecting a WiFi hot spot that has a registered latitude/longitude.  

Cell Tower triangulation and WiFi is fairly fast, but not very accurate.  When you bring up a map on your phone it will first use cell tower triangulation for its position.  When the GPS receiver gets a fix it will switch to using the GPS.  If you are indoors where GPS signals can't reach then it might never switch to using GPS.  That's why your position on the map may change significantly (and several times) during the first minute or so of using your phones map.