It means that access to your paper (or other research output) is free and available to anyone, anyone can read and download your paper. Normally, this should also be accompanied by few restrictions on copy and use by others, for more information see Licensing below.
For a more formal definition, you might want to have a look at the Berlin Declaration on Open Access to Knowledge in the Sciences and Humanities:
Establishing open access as a worthwhile procedure ideally requires the active commitment of each and every individual producer of scientific knowledge and holder of cultural heritage. Open access contributions include original scientific research results, raw data and metadata, source materials, digital representations of pictorial and graphical materials and scholarly multimedia material.
Open access contributions must satisfy two conditions:
The author(s) and right holder(s) of such contributions grant(s) to all users a free, irrevocable, worldwide, right of access to, and a license to copy, use, distribute, transmit and display the work publicly and to make and distribute derivative works, in any digital medium for any responsible purpose, subject to proper attribution of authorship (community standards, will continue to provide the mechanism for enforcement of proper attribution and responsible use of the published work, as they do now), as well as the right to make small numbers of printed copies for their personal use.
A complete version of the work and all supplemental materials, including a copy of the permission as stated above, in an appropriate standard electronic format is deposited (and thus published) in at least one online repository using suitable technical standards (such as the Open Archive definitions) that is supported and maintained by an academic institution, scholarly society, government agency, or other well-established organization that seeks to enable open access, unrestricted distribution, inter operability, and long-term archiving.
Some help with terminology
Open Access Journals
These are journals that publish every article with open access. If you pay a publication fee (or article processing charge, APC), this will automatically cover open access to your article. Normally, your article is then published under a Creative Commons License (see below).
Here is a very useful resource if you would like to find an open access journal in your research area or want to find out whether your favourite journal is open access:
These are journals that do NOT publish every article with open access but offer the option to make your article open access if you pay a fee. Note that this fee will have to be paid in addition to the publication fee/ APC that you have to pay for publication in that journal. Also note, that you might not necessarily retain copyright of your work. Copyright might still remain with the journal publisher even if you have chosen to pay the open access fee. In most cases, there are two different routes to open access in hybrid journals: gold and green open access.
Gold Open Access
This means that your article is immediately available with open access. It also normally means that the article is published under a Creative Commons License (see below) but always check the journal's policy.
Green Open Access
This allows self-archiving of the final version of your article in an institutional depository (such as Oxford University’s repository ORA) or on a preprint server. In most cases self-archived versions of your article can only be made publicly available after an embargo period and copyright is transferred from the author to the publisher. Again, you will need to check the journal's policy.
Every publisher handles this in their own way, so always make sure you have a look at the journal's policy. If you would like to publish open access according to the definition above, you should not transfer copyright to the publisher and your work should be published under a Creative Commons License. Here is an explanation of the different CC licenses (https://creativecommons.org/share-your-work/licensing-types-examples/licensing-examples/):
CC BY (attribution alone): This license lets others distribute, remix, tweak, and build upon your work, even commercially, as long as they credit you for the original creation.
CC BY-SA (attribution, share alike): This license lets others remix, tweak, and build upon your work even for commercial purposes, as long as they credit you and license their new creations under the identical terms.
CC BY-ND (attribution, no derivatives): This license allows for redistribution, commercial and non-commercial, as long as it is passed along unchanged and in whole, with credit to you.
CC BY-NC (attribution, non-commercial): This license lets others remix, tweak, and build upon your work non-commercially, and although their new works must also acknowledge you and be non-commercial, they don’t have to license their derivative works on the same terms.
CC BY-NC-SA (attribution, non-commercial, share alike): This license lets others remix, tweak, and build upon your work non-commercially, as long as they credit you and license their new creations under the identical terms.
CC-BY-NC-ND (attribution, non-commercial, no derivatives): This license is the most restrictive of our six main licenses, only allowing others to download your works and share them with others as long as they credit you, but they can’t change them in any way or use them commercially.
You may or may not be aware of controversies around the business model of large publishers, such as Elsevier, Springer Nature, Wiley-Blackwell, Taylor & Francis, or SAGE.
So far, this model has been to let authors (i.e. their institutions or funders) pay publication fees/ APCs to get a paper published in a particular journal and then let institutions pay for access to this article so that the authors' colleagues can read it. You might think that this sounds like a huge waste of taxpayers' money and that immediate open access to all research output is a worthwhile goal.
Rather than paying the extortionate fees that traditional publishers demand for gold open access of your article, you might want to have a look at these journals/ publishers, which offer open access immediately and are either non-profit publishers and/or re-invest profits in research or education: