As already mentioned, work certificate is a blunt translation of Arbeitszeugnis (reference letter). It is a standard thing to require for regular employments in Germany. The quoted sentence looks as if some bureaucrat bluntly translated the boilerplate of a regular German job ad into English and lacked the experience to adapt it to an international audience.
What is important for you is that German applications usually come with the pertinent certificates, references, etc. for every major item on your CV.
This will usually be your bachelor’s and master’s transcripts and diplomas (if already available).
This may imply letters of recommendation, if not mentioned otherwise in the job ad; however before you waste time on this, I would just ask them.
If you spent any extended time of your life doing something other than studying and you already have a certificate for this, you might as well include it, but I wouldn’t worry about organising anything before you got an offer (see below).
For example, my applications never included my poster award or the certificate for the year I spent in compulsory military/social service.
If you adhere to the above, I consider it very unlikely that your application will be dismissed for failing to include some certificate.
Your application will probably go straight to the professor or somebody else who can reasonably handle international applicants.
They will not dismiss your application for such a reason, but tell you if they want anything else.
Of course, there are exceptions, but in that case you probably do not want the position anyway.
In general, the main place for certificates is later in the hiring process, when you got offered the position and the administration will prepare your actual contract.
They will then usually tell you specifically what certificates they need, amongst others to calculate your salary.