When people first started to use the Web, they found that they needed to write web interfaces to their databases, or add databases to drive their web interfaces. Whichever way you look at it, they needed to connect to the databases in order to use them.
CGI is the most widely used protocol for building such interfaces, implemented in Apache's mod_cgi and its equivalents. For working with databases, the main limitation of most implementations, including mod_cgi, is that they don't allow persistent connections to the database. For every HTTP request, the CGI script has to connect to the database, and when the request is completed the connection is closed. Depending on the relational database that you use, the time to instantiate a connection may be very fast (for example, MySQL) or very slow (for example, Oracle). If your database provides a very short connection latency, you may get away without having persistent connections. But if not, it's possible that opening a connection may consume a significant slice of the time to serve a request. It may be that if you can cut this overhead you can greatly improve the performance of your service.
Apache::DBI was written to solve this problem. When you use it with mod_perl, you have a database connection that persists for the entire life of a mod_perl process. This is possible because with mod_perl, the child process does not quit when a request has been served. When a mod_perl script needs to use a database, Apache::DBI immediately provides a valid connection (if it was already open) and your script starts doing the real work right away without having to make a database connection first.
Of course, the persistence doesn't help with any latency problems you may encounter during the actual use of the database connections. Oracle, for example, is notorious for generating a network transaction for each row returned. This slows things down if the query execution matches many rows.
You may want to read Tim Bunce's "Advanced DBI" talk, at http://dbi.perl.org/doc/conferences/tim_1999/index.html, which covers many techniques to reduce latency.