When working with Subversion, you typically deal with two different parts in your day-to-day life: a working copy and a repository. Consult the About Subversion chapter if that doesn't sound familar to you.
Both a working copy and a repository intrinsically are bound to a specific version of the Subversion software, but both are independent and can be different. More on that in a minute.
You likely don't notice all of that, and don't need to. You use a so-called Subversion client, like Versions to interact with your working copy and your repository, and that client usually talks to the repository located on some remote server.
The repository is the part often residing on some server in the cloud. Good news is that the particular version of that part is most of the time not of great relevance. Newer versions may have more features, but the basics have been fairly stable through the years, so you should not notice any problems. Find out more about interoperability at the Apache Softwaer Foundation site.
The potentially trickier part is your (local) working copy. Working copies have stricter requirements and may be incompatible with your client.
As long as you are just using Versions, there's no need to bother. If Versions prompts you to upgrade your working copy, just do it.
As soon as you're trying to access a working copy with multiple clients, like Versions and the Subversion command-line tools, or some other graphical client, it's important that those clients are compatible.
The Versions Preferences window shows the version of the subversion library built ito Versions, and tries to query the version of the Subversion command-line tools that may be installed on your computer. If those aren't compatible and you want to work with the command-line, you may need to upgrade the command-line tools, or look for a more recent version of the Versions app.
Working copies can be upgraded to support a newer (Subversion) version, but not be downgraded again. Versions may prompt you to upgrade a working copy in order to be able to access it.
If you are not sure that will compatible with your entire workflow, please make a backup of your working copy before doing so, or don't upgrade until you can savely make that decision.