In one sentenceA fixed place of business through which a non-resident carries on its activity in the Kingdom, such as a branch or office, so the income connected to it is taxed locally.
Simply put
Having a fixed place of business turns a non-resident from a party subject to withholding into one that registers and files a return on that place's profits.
That is why the issue matters when contracting with foreign companies that carry out long projects inside the Kingdom.
Example
A foreign engineering company opened an office in Riyadh with staff who manage its projects in the Kingdom. The office is a permanent establishment, and its profits are subject to income tax in the Kingdom.
Don't confuse it with
Non-residentEvery permanent establishment belongs to a non-resident, but not every non-resident has a permanent establishment.