If your Bugzilla has been customized or uses extensions, you will need to make your customizations or extensions work with your new version of Bugzilla. If this is the case, you are particularly strongly recommended to do a test upgrade on a test system and use that to help you port forward your customizations.
If your extension came from a third party, look to see if an updated version is available for the version of Bugzilla you are upgrading to. If not, and you want to continue using it, you'll need to port it forward yourself.
If you are upgrading from a version of Bugzilla earlier than 3.6 and have extensions for which a newer version is not available from an upstream source, then you need to convert them. This is because the extension format changed in version 3.6. There is a file called extension-convert.pl in the contrib directory which may be able to help you with that.
This documentation undoubtedly has bugs; if you find some, please file them here.