What is the software that the Magento server needs to run?

The full list of software is listed in System Requirements but here are the essentials:

• Web server for providing access to web pages - Currently, we’ve documented Apache and plan to document other web servers in the near future.

• Database management system for long-term data storage and retrieval - We support MySQL.

• PHP - PHP is an open source scripting language suited for web development because it can be embedded in HTML (the language of the web).

  For more information, see the PHP manual or the PHP Wikipedia page.

If you use a hosting provider, they might already have installed this software. Contact them if you’re not sure.