There are two fundamental methods for scaling server infrastructure. They can be scaled up, or they can be scaled out. In the former, sites are progressively moved from lower spec servers to higher. Typically a site or group of sites might move from shared hosting to a low-powered dedicated server and then to successively more powerful servers. Scaling up is also frequently referred to as vertical scaling.
The second method, scaling out or horizontal scaling is different. Imagine a group of sites hosted on a relatively low-powered server. As the sites grow in popularity and their traffic increases, eventually the server will reach peak capacity. Load beyond this point will cause the server to falter: usually it’ll be the RAM that gives out first. The server worker processes will multiply to the point at which there is no more memory available: the server will start queueing requests and swapping out memory to disk. This is a bad situation for a server to be in because it significantly degrades site performance.