Short answer: If you have to ask, you should probably stick to the stable release.
What are nightly builds?
As the name implies, nightly builds are generated every night from the current master branch of the source repository. They are meant to allow a wider audience to more easily test new features.
What are the dangers when using nightly builds?
Nightly builds like all software have bugs. Because they have new not yet widely tested features you must expect a higher number of bugs. This includes critical bugs. (Nightly builds are meant to be there to expose new features to a wider audience. The hope is that this will increase the quality of the stable release.)
Users of nightly builds should be aware of this danger.
Another additional danger is that nightly builds might produce files that can not be used by any version different to the one used to produce them. (Mainly older versions might not be able to use these files.) This fact might lock you into using nightly builds until your project is finished.
It might also make it harder to share your project with others. (Nightly builds might not exist for the operating system someone else uses. Or they might not be allowed to install nightly builds for policy reasons.)
There is little to no documentation for nightly builds. If there is a large change in workflow you might be on your own to find out how to use the new tool. To reduce the surprise, it is a good idea to follow the mailing list. And watch out for new announcements on the kicad webside. (blog posts) Or possibly even watch the git repo and read the commit messages. main source repo, github mirror
What are the benefits of using nightlies?
You get more features.
You can help make future kicad releases better by finding and reporting bugs.
What about after a feature freeze or with release candidates?
Note: Nightlies from after 14. March 2019 are no longer part of the of the v5 release cycle. (They are part of the v6 development.)
As there are no no features added in this time period, all files generated by such builds should be compatible. Especially between the release of the first release candidate and the stable release.
There might still be a higher number of bugs then in a stable release and the documentation will probably not yet reflect the full feature set.
Small changes to the official library and to the graphical interface might still happen in this time frame.