To quote the material that you link:
The system makes it possible to protect a mark in a large number of countries by obtaining an international registration that has effect in each of the designated Contracting Parties.
Basically, it is the moral equivalent of autofiling an application in all or many member jurisdictions at the same time, which are then individually evaluated like any other domestic trademark application.
Otherwise, to trademark something in many countries around the world, you'd have to fill out hundreds of nearly identical applications that would have slight quirks particular to each country which would cost applicants more money since they'd also have to hire lawyers separately in each country they wanted a trademark to be effective in. This would also leave applicants who didn't go through those hoops with trademarks that weren't valid in large parts of the world. This is problematic in a global economy where many firms, even small ones, do business all over the world.