SQLite is a C library, written by D. Richard Hipp and others, that implements an embeddable SQL database engine. Programs that link with the SQLite library can have SQL database access without running a separate RDBMS process. The distribution comes with a standalone command-line access program (sqlite) that can be used to administer an SQLite database and which serves as an example of how to use the SQLite library.
SQLite is not a client library used to connect to a big database server. SQLite is the server. The SQLite library reads and writes directly to and from the database files on disk.
SQLite is used by Mac OS X software such as NetNewsWire and SpamSieve.
When you download SQLite and build it on a stock Mac OS X system, the sqlite tool has a very primitive command-line editing facility. This build of sqlite uses the GNU readline library, which provides fancy command-line editing (using, e.g. Emacs key bindings) as well as a command history. Software built using the included libsqlite.a library does not link with readline and thus is not tainted by the GPL.