MySQL is small, free, easy to use, supports many popular sql statements, including joins.
Oracle is large, expensive, complex to use, but supports just about every sql statement you can think of.
Basically, MySQL is a low-budget, limited functionality database that is
perfect for small to medium size applications.
It is installed in 3 minutes, plugs right into php,perl etc.
But....
If you want to have all sql functions (sub-selects, views etc)
or you are planning on using a huge database with high load, you'll have to move to something more powerfull, like Oracle or Informix.