HyperDB is a replacement for the standard wpdb class which adds the ability to use multiple databases. HyperDB supports partition of data as well as replication.
This involves moving different tables or different parts of the database into different databases, and normally on different servers. This allows you to scale an application by adding more database servers, so your data could be spread across several servers.
HyperDB allows you to specify which data resides on which servers.
Replication involves having one database server act as the master (the central copy of all data) and other servers act as slaves (each with a copy of the data). All the database writes must go to the master server, but database reads can be sent to slave servers, thus spreading the load amongst multiple servers.
HyperDB allows you to split database writes and reads and assign each to an array of servers.
HyperDB allows multiple servers to be configured and multiple routes to servers. If the first server can't be accessed the second server is tried, if that's down the third server, and so on. This allows for failover from internal nics to public nics to remote datacenters, etc.
For support / discussion / questions with HyperDB join the mailing list.