I am pretty sure that this is not an epson menu or an Adobe menu. I am guessing here that this is also not part of Epson printer installation settings for the operating system settings (mac or windows.) My guess is that this would by a printer setting in a third party application- where you can specify what printer you are using and maximize the settings for the third party program.
This is part of the Epson driver, nothing to do with Adobe or Apple. I think it dates back to days when computers were slower .. at this point with modern computers I don’t think there will be any difference.
here is the official text from the user manual
“Processed by Printer allows the halftone output processing to be performed by the printer. This feature speeds processing, especially for older computers, and ensures that the printer runs at maximum speed. This involves image compression and decompression, and does not affect the quality of your output.”