In Unix/Linux dot-files refers to files/directories with a . prepended to their name. Examples are ~/.bashrc, ~/.bash_profile, etc. The leading dot . is used as an indicator by software like bash and nautilus to not list these files normally but only when they are specifically requested like pressing Ctrl+H in Nautilus. This is because, generally, dot-files are used to store configurations for different applications but they are sometimes used otherwise as well. For example Mozilla creates a .mozilla folder which contains their configuration files as well as browser cache.

People tend to backup & also share their dot-files so others can boot-strap their own applications using those configuration files. An example of a site dedicated to sharing dot-files is http://dotfiles.org.