"Open access is the free, immediate, online availability of research articles coupled with the rights to use these articles fully in the digital environment." (SPARC (the Scholarly Publishing and Academic Resources Coalition), https://sparcopen.org/open-access/)
Let's break that definition down:
There are multiple levels of open access.
Article Processing Charges (or APCs) are commonly associated with open access publishing. Some journals charge authors in order to have articles published open access, in order to offset the loss of revenue from making articles available for free.
It is important to remember that charging an APC does not make a publisher a "vanity press." Articles still undergo peer review and editing like they would in a non-open access journal.
However, the use of APCs has led to an explosion of "predatory publishing," where publishers charge APCs but do not provide peer-review, editing, or indexing of published articles. (View the Predatory Publishing page of this guide for more information.)
SPARC also provides an good outline of the traditional, non-open access publishing model: