I am aware that Firefox has nightly builds available at https://nightly.mozilla.org/ and was wondering what the difference was between the stable and nightly builds. Are they safe to use or are they primarily for beta testing?
Nightly builds feature the absolute latest changes, and are considered unstable. They are the most buggy, and will result in a higher crash count than stable Firefox Releases. They are to be used for seeking bugs, and then submitting them to Mozilla developers, so that the Beta and Release channels do not suffer from such bugs.
Nightly is usually many versions ahead - Currently on 9. So you will be seeing features added long before others, but at the risk of crashing more, and potentially broken parts of Firefox. I can confirm this by using x64 Nightly and not being able to use Flash properly anymore (Crashes x64 Flash)
They are to be used at your own risk and discretion. As they say, "These builds are for testing purposes only.", so don't count on Nightly when working.
They're for those who want to live on the bleeding edge and don't mind instability as part if their daily browsing life. Maybe they're developers or testers.
People who want mostly stable builds should use Firefox's Beta Channel. If you want to be in on the newest features with the occasional crash, there's the Aurora Channel.
You can choose from the channels at http://www.mozilla.org/en-US/firefox/channel/