A lot of data doesn't change very often; and a lot of data can tolerate propagation delays on change. When you have an extremely high read volume against such data sets, it can be economical to cache the entire data set and distribute it periodically to the fleets of machines that require access, as opposed to servicing individual reads over a network. Provides lower cost and latency, while supporting a higher volume of reads and higher availability, at the expense of engineering cost and propagation delay.
Take sendmail: people would have their email-aliases in a /etc/aliases file, with a simple ascii-format, lines formatted according to: "<key>: <values...>". The "newaliases" command then would convert the content of the ASCII file /etc/aliases into the binary (originally: Berkeley db) /etc/aliases.db.
As far as I know, CDB was developed initially for qmail, DJBs email-daemon, for exactly that purpose.
Another example for this is the "Yellow-Pages" (yp) / NIS directory services to distribute usernames/userids/groups/... in a UNIX cluster or network. ASCII files were converted into e.g. /var/yp/DOMAIN/passwd.byname, a .db-file where keys are the usernames from /etc/passwd and values were the full ASCII lines from /etc/passwd, same goes for passwd.byuid, group.byname, and so on. All for fast indicing, so that the network server didn't have to repeatedly parse /etc/passwd.
It's not really the same thing, though. CDB provides a single key -> value mapping in a single file, with updates by replacing the entire file; SQLite is a relational database with updates, locking, transactions, SQL, etc.