A single database server for a small set of applications and data has historically worked well. However, when exposed to a large, public user base, the only way to increase the capacity of these servers is to upgrade them to a more expensive server.
To improve capacity, move the database software to another single machine with more memory, more disk space, and more processors. This is "vertical scaling". The drawback to this approach is that it may require downtime. There's also a ceiling on the performance that can be obtained from a single machine. (See Herb Sutter's The Free Lunch is Over).