MySQLi
MySQLi is a better and faster MySQL extension. You can use any existing MySQL database. The installation script cannot create a database for you. On the next screen you will have to provide a database name, a database user and a password. Check your server documentation for details on how to create a new database and define user privileges.

PDO SQLite (SQLite 3)
An SQLite database consists of a single file. The installation script will try to create a new directory and a database file. If not possible you will be prompted to create the directory manually and CHMOD* it to 777.   * CHMOD means to change permissions/attributes of a file or a directory on Linux and Unix based systems. This can be done with any FTP program.