It allows the download of additional fonts to the printer.

Many laser printers have an inbuilt language called Postscript, which is stack based. More memory means you can have a bigger stack, which means that you can process more complicated documents, and they can print faster.

Postscript can also make use of pre-defined libraries which can be downloaded to the printer - these can be stored in the additional memory, so don't need to be downloaded for every printout.

In the case of an all-in-one printer, when copying it allows more pages to be stored before printing has to start.

And in the case of a network printer, many will allow documents to be spooled to the printer but held in the printer's memory in a "mailbox" specific to that user or group. The user will instruct the printer to start printing once they are there to collect it.
Hence no more cases of people picking up the wrong printout, or re-shuffling part-completed printouts, or scrap pages being left all over the printer room.