The error message doesn’t state it because there could be several different reasons for that type of error. Rosetta 2 is required for Local’s Apple Silicon build due to the Nginx and MySQL Lighting Services compiled on the Intel architecture, as mentioned in our Install Local help article here.
Some other things that can create that error for example are things like security applications or other developer programs getting in the way.
Regarding Rosetta, if you need help with how to install that there are some details on the thread below that might be helpful!