It is a way for the magazine to notify the US Mail service that they want undeliverable mailings to be handled a certain way- specifically that whatever address change or forwarding has been set up between the receiving person and the USPS be forwarded to them, so that they can send the magazine to the new address directly.
IE, if the magazine didn’t write “Change Service Requested” and the subscriber moved, the postal service would just junk the undeliverable magazine and not tell the magazine they did so.
The USPS charges companies when they do this, and so “Change Service Requested” lets them know that the magazine is down for those service charges.