SQLite is a small, fast, embeddable database. What makes it popular is the combination of the database engine and interface into a single library as well as the ability to store all the data in a single file. Its functionality lies between MySQL and PostgreSQL, however it is faster than both databases.
In SQLite, author Chris Newman provides a thorough, practical guide to using, administering and programming this up-and-coming database. If you want to learn about SQLite or about its use in conjunction with PHP this is the book for you.
SQLite is one of the fastest-growing database engines around, but that's growth in terms of popularity, not anything to do with its size. In fact one of SQLite's greatest strengths is that it is extremely lightweight indeed yet still manages to retain a large number of features.