WordPress provides a free home for any plugin at the WordPress Plugin Directory, found at http://wordpress.org/extend/plugins/. It simply represents a frontend to the WordPress SVN repository found at wp-plugins.org.
Subversion (also known as SVN) is software that allows you to easily store and manage your plugin projects (you can find a SVN FAQ at http://subversion.tigris.org/faq.html).
Once in the WordPress SVN, everyone will be able to check out (download) a copy of your plugin, but only you, as a plugin author, will have the ability to commit changes to the plugin in the repository.
In order to gain write access to the repository, you need to fill out the Request form found at http://wordpress.org/extend/plugins/add/.
You will need to provide:
A plugin name
A short description
An URL to the plugin homepage
The access will usually be granted in a couple of days, and the best way to use the time while you wait is to polish...