Before we get into the ins and outs of how the system works and what's new from a user standpoint, it's worth highlighting the major changes Apple has made to the guts of Mac OS X. Although nothing will deter some people from claiming Snow Leopard is a service pack, we can't recall any time when a free operating system service pack had major internal upheavals along the lines of this Apple release.
Aside from QuickTime, which is discussed later, Apple flags 64-bit, Grand Central Dispatch and OpenCL as big news. The first of those is the continuation of a transition that began in 2003, and Mac OS X now ships with a 64-bit kernel. Only Xserves currently boot into this mode, however, due to a lack of 64-bit device drivers. Therefore, 64-bit is largely something for Apple's future; although with Apple shipping most of its apps as 64-bit, it's clear the transition will happen sooner, rather than later. Perhaps Mac OS X 10.7 'Scraggy moggy' will boot the 64-bit kernel by default.
Grand Central Dispatch and OpenCL deal with advanced threading (to take full advantage of multicore processors) and utilising the power of GPUs for general-purpose computing, respectively. While exciting for developers, both technologies won't be exploited until hardware and software evolve, and so they're of little immediate use to the typical Mac user.
However, some changes will make a difference right away. Apple's streamlined many apps (dropping PowerPC code - Snow Leopard is Intel-only), dumped printer drivers from the default install and compression is used heavily. Expect to get back several GB post-install.
GETTING SMALLER: Check your drive's free space after installing Snow Leopard for a nice surprise