It refers to the process of prosecuting an application with the trademark registration office where registration for the mark is sought in accordance with established rules and guidelines of that jurisdiction.

While the application forms contain general guidelines, the office does not advise in advance whether your specific mark is registrable.

Each application is decided on its own facts in accordance with the substantive laws of that jurisdiction.

Needless to say, the prosecution of a Trademark Registration is best done by an IP professional who is more familiar with the local laws and procedures of that specific jurisdiction where registration of mark is sought.