A word after function arguments braces
That's impossible to tell without looking in the source code for that SDK.
However it will just be a pre-processor macro which probably expands out to one or more attributes, some of which may be specific to the XTensa LX106 compiler.

Update after your edit:
It places the function in the privileged_function section. That section is then placed into a specific area of memory by the linker.
To further examine what it does you will have to look in the linker script to see how it handles that section, and what that means from the chip's perspective, by cross-referencing that with the chip's technical datasheet.