ftp stands for file transfer protocol. It is the standard program to use to move files from one computer connected to the Internet to another. Normal ftp requires that you have an account on the remote computer. You type ftp address where address is the IP address or name of the computer to which you want to connect (e.g. ftp pdb.pdb.bnl.gov would connect to the Brookhaven lab ftp server). The computer will then prompt you for a username and password and if all goes well, log you in. You can move around the remote computer filesystem using the standard Unix commands cd to change directories and ls to list the contents of a directory. The commands get and put allow you to transfer files from/to the remote computer. It is usually best to issue the command bin before doing any transfers as this avoids corruption of binary files.
Anonymous ftp allows you to log into a remote computer on which you do not have an account. For security reasons, computers that support anonymous ftp will only allow access to a protected region of their filesystem. Anonymous ftp is a way for someone to make software or data files available to the world without having to email them to people or send tapes etc. I have set up anonymous ftp on the computer barton.ebi.ac.uk to distribute software from my group and this works well. To log in to an anonymous ftp site you use the username anonymous and your email address as the password (the username ftp also usually works.
There are many hundreds of ftp sites around the world. Some are small and very specific like mine, others act as archive and distribution points for thousands of programs and data files. You can search to see if a particular file is on an ftp server by using the program archie from a normal terminal, or xarchie (if you have a terminal that supports X-windows). Currently, the easiest way to perform an archie search is via the Mosaic program - see below.