Just as Photo can be compared with PhotoShop, so Publisher will be seen as a challenge to Adobe's InDesign - not the least because you buy it outright. No monthly rental!
A feature which Affinity kept close to their chest until the release of Publisher is that it's closely integrated with Photo and Affinity's graphics application Designer. This means that if say, you own both Publisher and Photo, you can make edits to images using the full power of Photo from within Publisher - and access is instantaneous.
If you're thinking of publishing your work either in printed form or as pdf, Affinity Publisher is worth a look.
More details can be found here.