Why would your printer need your router’s id?
Maybe it thinks the router is under 18?
If it’s a wireless printer, it needs to get on the network so you can print wirelessly. The printer has to recognize the router, and the router has to recognize the printer. Plus, a password is involved if the network is secure.
I’m not all that familiar with this stuff even though we have a HP wireless printer, so I’m sure there’s more to it. It is nice though, to print from the laptop or cellphone anywhere in the house. The printer shows up on the list of printers that are available for your particular print program.