I think the idea of that document is you to put "cheap" databases in front of the "expensive" databases to reduce costs.
For example. Let's assume you have an "expensive" db...something like Oracle, or DB2 or even MSSQL (more realistically it's probably more of an issue with a legacy DB system that is not supported much or you need specialized resources to maintain). A database engine that costs a lot to purchase and maintain (arguably these are not expensive when you take all factors into consideration. But let's use them for the example).
Now if you suddenly get famous and your server starts to get overloaded what do you do? Do you buy a bigger server and migrate all your data to that new server? That could be incredibly expensive.
With the tiering solution you put several "cheap" databases in front of you "expensive" database to take the brunt of the work. So your web servers (or app servers) talk to a bunch of MySQL servers, for example, instead of directly to the your expensive server. Then these MySQL servers handle the majority of the calls. For example, they could handle all read-only calls completely on their own and only need to pass write-calls back to the main database server. These MySQL servers are then kept in sync via standard replication practices.
Using methods like this you could in theory scale out your expensive server to dozens, if not hundreds, of "cheap" database servers and handle a much higher load.