"Aminet is a set of interconnected FTP sites and other
file accessing services for Amiga software."
--Aminet help file, http://www.aminet.net/info/www/readme.html
Aminet is the primary repository for Amiga freeware, shareware, e-texts, modfiles, images, and so on. It is simply the place to go for non-commercial Amiga software, as well as demos for commercial packages, drivers, music in the various Amiga mod music formats (like protracker, fasttracker, intuitracker, and med/oktamed), and various other files.
Aminet is available from various mirrors worldwide. For more information, or for a mirror near you, visit http://www.aminet.net.
From an article on USENET: 
From: Urban D. Mueller (email@example.com)
Subject: comp.sys.amiga.misc New anon ftp site amiga.physik.unizh.ch
Date: 1992-01-19 17:32:27 PST
We have a new anonymous ftp site at amiga.physik.unizh.ch 220.127.116.11,
located in Zurich, Switzerland. It has many AmigaDOS files and it is the
official Amiga UNIX anon ftp site (although not much is there yet). As a
special feature it creates file lists like the one below from all uploads
that have a special .readme.
(Message truncated to save space)
The original incarnation of Aminet first went public January 19, 1992, as a "borrowed 25 MHz 68030 computer at the end of the world (ie. Switzerland) with only 50MB of harddisk space available for uploads"  was donated by Commodore of Switzerland, and owned by the local Amiga User's Group (UG, or in their case, ICU.) The original archive was made up of a small set of files originally stored on this machine, plus the amiga archive from ab20.larc.nasa.gov.
The site had two major problem; 50MB was not enough, even in those days, and locating the system in Switzerland created a major bandwidth bottleneck. Peter Sjostrom of IRC #amiga on EFNet had a site in Sweden that was capable of sustaining a larger than 50MB archive, and amiga.physik became the new home of Aminet. Donations (Half of them from Walnut Creek Inc./Walnut Creek CDROM) purchased a 1.5GB disk, quite a decent amount of space in those days.
Aminet reached 5,000 files on September 24, 1993  and 10,000 files on October 14th, 1994.  On May 16th, 1996, Aminet became the world's largest collection of freely distributable software with 29,000 files, and 30 mirrors. 
 USENET News Article knk8ouINNdst%40agate.berkeley.edu. Urban D. Mueller, [comp.sys.amiga.misc] New anon ftp site amiga.physik.unizh.ch. 1992-01-19 17:32:27 PST
 Email conversation with Urban Mueller, June 2, 2002.
Aminet files  docs/misc/5000.txt,  docs/misc/10000.txt, and  docs/misc/30000.txt