It should be noted that this English phrase is expressly defined in a wide range of conventions, model treaties and national and supra-national legislation. Thus, the German concept of Betriebsstätte, with its very specific meaning under German law, will not necessarily line up with this English phrase translation since the latter will have a different shade of meaning depending on the law in question. It is, however, the universally recognized translation, and in the end, an experienced (tax) lawyer should understand that there will be nuanced substantive differences in a given context.
There are multiple definitions - click on the translation that matches your context.
a fixed place where a business entity's work is done (either mostly or partly)
Employees are generally considered to report for work at an employer's permanent establishment if they go to that location regularly.
a concept that allows the taxing by a state of non-residents operating a business from within its jurisdiction
A firm shall be said to have a permanent establishment in a country if it employs an agent there to act on its behalf regularly.