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