Open Access (OA) research is research that "is digital, online, free of charge, and free of most copyright and licensing restrictions."
The term "Open Access" was first formulated at the Budapest Open Access Initiative (BOAI) in February of 2002. The initiative grew out of a small meeting in Budapest by the Open Society Foundations that took place in December of 2001. The aim of the meeting was to support an international effort to make research articles freely available via the internet. The original BOAI declaration defined open access to scholarly literature as consisting it its "free availability on the public internet, permitting any users to read, download, copy, distribute, print, search, or link to the full texts of these articles."
The BOAI was followed in 2003 by the Bethesda Statement on Open Access Publishing and the Berlin Declaration on Open Access to Knowledge in the Sciences and Humanities.
There are different ways in which authors can make their work Open Access. While publishing in an Open Access journal may be the first thing to come to mind for many researchers (i.e. Gold OA), you can also make work published in regular subscription journals Open Access by depositing it in disciplinary or institutional repositories (i.e. Green OA).