Here is how I explain available memory's impact on DB operations. Bert's may well be more erudite.
Databases consume part of memory to cache (hold) the information that is requested. This can be described as pages, trees, leaves depending on several factors.
That memory is like the available workspace in a shop; whether you work on bikes, quilts, machine parts, furniture - how much you can work on is limited by the workspace. You can have acres of storage space(think hard drive space), but that doesn't bear on your usable space (setting aside virtual memory).
So, in that workable space, the DB brings information out into the workspace as it is requested. Over time, data is aged, and as the space fills up, some information that is less used is put away, but performance actually improves if it is drawn from information already in the workspace.
Every time the server is restarted, the process of bringing data into the workspace starts over.
