ETL is commonly used in data warehousing applications.
For example, you might have an Oracle or Sql Server order processing system. This might keep all the data until the order is shipped, but you wouldn't want years worth of old orders clogging up the system.
Additionally, you might have several systems like this in your company, all developed independently of each other.
So, to consolidate the historical data, you might set up a data warehouse where the data from all of these disparate systems end up, allowing you a nice place to do reporting, planning, data mining, etc.
Since all the data sources are different, and the kinds of data you want to store long-term might differ than the data you have in the smaller databases, you set up an ETL system to convert and manage the data flow.