CiviCRM Raw Data Files
The answer rather depends on what data you have in CiviCRM and what you want to export.

One option is to export the data as a CSV file as Demerit says. This will allow you to export certain types of data - for example: contacts, event participants, activities.  You can do this via advanced search. See the manual for more details: Exporting your contacts.

Another option is to access the data directly from the database. This gives you more control to access the data that you need but would require some understanding of the database structure and SQL. If you have access to phpMyAdmin you will be able to export the SQL data using this (log in to phpMyAdmin and click on the Export tab). Alternatively your website hosting company may have a tool that allows you to export the SQL - you could contact them for help.

A third option to export the data via the API which would require some programming.