This is what I think, but if anyone understands it differently please correct me.

Vertical scalability refers to scaling within a single instance. More users join and they post more content, increasing the amount of disk space needed to hold that memory, network bandwidth to handle many users downloading comments and images at once, and processing power.

Horizontal scaling refers to the lemmyverse growing because of the addition of new instances. The problem in this form of scaling is due to the resources that an instance has to use due to its interactions with other instances. So, you may create a small instance without a lot of users, but the instance might still need a lot of resources if it attempts to retrieve a lot of information (posts, comments, user information, etc) from the other larger instances. For example, at some point a community in lemmy.ml might be so popular that subscribing to that community from a small instance would be too much of a burden on the smaller instance because of the amount of memory required to save the constant stream of new posts. The horizontal scaling is a problem when the lemmyverse becomes so large that a machine with only a small amount of resources is no longer able to be part of the lemmyverse because its memory gets filled up in a few hours or days.