Oracle is proprietary Database management system owned by Oracle corporation. It is SQL based database, it provides extensive programming interfaces and it is multimodel database. In general Oracle is widely used in the Transaction processing systems, Oracle database also provides distributed database management system. Oracle is known for the fastest and most scalable database available in the market. It also provides the rich admin interface.
The database is free and open source with a commercial license available (MySQL is now owned by Oracle after they bought Sun). Common applications for MySQL include php and java based web applications that require a DB storage backend, e.g. Dokuwiki, Joomla, xwiki etc
MySQL has one major advantage, since it is free, it is usually available on shared hosting packages and can be easily set up in a Linux, Unix or Windows environment. If a web application requires more than database, requires load balancing or sharding