Outreachy (formerly the Outreach Program for Women, OPW, or FOSS OPW) is a full-time internship program for women of any age and background to spend 3 months contributing to a free and open source project.
Wikipedia article with a lot of detail.
History
The GNOME Foundation first started the internships program with one round in 2006, and then resumed the effort in 2010 with rounds organized every half a year. In the May-August 2012 round, the Software Freedom Conservancy joined the Outreach Program for Women with one internship with the Twisted project. In the January-April 2013 round, many other FOSS organizations joined the program, and new rounds continue to have many non-GNOME projects offering internships.
The program's GNOME wiki page has details about previous, current, and upcoming rounds.