The most widely accepted definition of open access comes from Peter Suber:
"Open-access (OA) literature is digital, online, free of charge, and free of most copyright and licensing restrictions."
Suber's book on open access, conveniently titled Open Access, examines the topic in more detail and is available digitally and free of charge online:
Open access helps make the results of academic research available to those who do not have the resources to pay hefty costs to access research articles, books, and more through traditional venues such as academic libraries and journal subscriptions.
There are several paths to open access. These paths are sometimes referred to by color.
Gold: Golden open access refers to articles published in fully open access journals and available without any delay or embargo or costs to the end user. Some golden open access journals will charge the author Article Processing Charges (APCs) to publish their article to make up for the lack of subscription fees.
Green: Green open access refers to articles that are "self-archived" and made available by the author. These can be pre-prints, like those found in arXiv, or the final published work. Green open access is usually completely free for the author and the end user.
Bronze: Bronze open access refers to articles that are available from their publisher, but do not have a Creative Commons license attached. At any point they may be made unavailable for free download.
Hybrid (Fine, this one isn't actually a color): Hybrid open access refers to articles that are made freely available in journals that are not fully open access. Articles published in this method generally require APCs.
The University of Mississippi Libraries offer a fund to support authors publishing in open access publications. More information and an application can be found on the Open Access Fund page.