It reduces the load simply because your instance handles most of the traffic, particularly compute/database. Currently media still goes to the instance of the poster, but there’s talks of also proxying and caching those locally, and CDNs like CloudFront/Cloudflare are a thing that can help a lot with that.
So lets say we have server A and B, both with a thousand users on them, totalling 2000 users. For the most part, A and B only have to handle their local thousand users, plus some extra traffic between them for federation. And assuming the users uses communities of both instances roughly equally, it also means that the load of hosting pictures is also spread out between the two instances.
Federating with other servers does add some load (and on theirs as well), because your instance is effectively ingesting all the remote communities’ data that your users have subscribed to. But ingesting that once is still much less demanding than thousands of users all requesting the same data. Your instance acts as a cache layer.
ActivityPub is also a push model. Remote instances push content to your instance, you don’t pull from them.