What is granular synthesis?

In short:
Granular Synthesis is a method by which sounds are broken into tiny 
grains which are then redistributed and reorganised to form other 
sounds.

Slightly more verbose:
Granular synthesis is perceived as a relatively recent development in 
sound synthesis, but it can also be seen as a reflection of 
long-standing ideas about the nature of sound. Quantum physics has shown 
that sound can be atomically reduced to physical particles(Wiener 1964). 
This physical form of sound was first envisioned by the Dutch scientist 
Isaac Beeckman (Cohen 1984). He explained that sound travels through the 
air as globules of sonic data. Later works including those by Gabor 
(Gabor 1946) and more recently Xenakis (Xenakis 1971), Roads (Roads 
1988), and Truax (Truax 1990) has evolved the particle theory of sound 
into a synthesis method whereby the natural sound particle is imitated 
and magnified, referred to as a grain. The grain is then layered with 
other grain, either cloned or extracted through a similar process as the 
original to create different sounds and sonic textures. The original 
intent of the process described by Gabor was to reduce the amount of 
data required to convery an audio human communication, necessitated by 
the low band width, but rising usage of telecommunication devices in the 
1940s (Gabor 1946). Gabor's research came into the hands of Xenakis, who 
recognised a musical application for this work (Xenakis 1971). Xenakis' 
first works involving granular synthesis were created by splicing 
magnetic tape into tiny segments, rearranging the segments, and taping 
the new string of segments together. After attending a seminar conducted 
by Xenakis on this topic, Roads began experimenting with this idea on a 
computer. His first experiments were extremely time consuming, even when 
rendering just a one minute mono sound (we are not talking minutes here, 
nor hours, but days, usually weeks, depending on scheduling and 
transferring). After reading an article about granular synthesis written 
by Roads in 1978, Truax began developping a way to create granular 
synthesis in real-time, first realised in 1986. From this point on, 
granular synthesis has slowly become available to a growing number of 
musicians and sound artists.