What makes an application memory bandwidth bound?

Question

This has been something that's been bothering me for a while: What makes an application memory bandwidth bound?

For example, take this monstrosity of a computer that calculated the 5 trillionth digit of pi (and later 10 trillionth digit). I was surprised that they choose the lower but faster 98 GB RAM at 1066 MHz instead of the larger but slower 144 GB at 800 MHz. This is especially surprising considering they are using 22 TB HD array to store the results from computation; more RAM means less need for hard drives.

Maybe its because I don't write applications for HPC servers, but how would RAM be the bottleneck? Are there any other non-HPC applications that usually run into this problem?