Memory barriers are designed to prevent reads and writes from being reordered by the compiler and being seen out of order on multi-core CPUs.
A typical pattern would be for thread A to write some data and a flag, and for thread B to read the flag and get the data. In this case you would insert a release barrier between writing the data and the flag, guaranteeing that the data write completes no later than the flag is written, and you would insert an acquire barrier between reading the flag and reading the data, to ensure that all the reads associated with the flag have completed.
In this pattern you should always see a release barrier paired with an acquire barrier and you should gate the data reads/writes with a single flag variable.
For more information on these semantics, take a look at the blog post: http://preshing.com/20120913/acquire-and-release-semantics
This function is available since SDL 2.0.6.