SQLite is used primarily for development purposes only because it is quite simple to setup a database without much frustration, however it is certainly less efficient in terms of concurrency (which is highly likely for web applications) than something like MySQL. So regardless if you use SQLLite in development or not, it is highly advisable to use MySQL (or something equivalent) in production.
For completeness sake, SQLite is also used in "all in one package" software (such as mobile development), in which you can easily bundle a SQLite file with your application.
As stated on SQLite Website:
SQLite is not intended to be an
enterprise database engine. It is not
designed to compete with Oracle or
PostgreSQL.
and
Another way to look at SQLite is this:
SQLite is not designed to replace
Oracle. It is designed to replace
fopen().
In terms of the benefits with Ruby, there really isn't much benefit as libraries/ORMs (i.e. Active Record) really abstract the differences between the two systems to make a consistent access layer in a single wrapper.