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.