A permanent establishment (for tax purposes) is a business premises of the foreign company in another country. The location must have the facilities to be able to operate as an independent business. Think of an office, workshop or shop.
There are also special permanent establishments; in practice these are referred to as fictional permanent establishments. The most important example of this is a construction project that lasts longer than 12 months. Another important example is the place of residence or the seat of the effective management of the business.