Magento System Requirements

Magento system requirements in base level, Magento will require the following software:

Supported Operating Systems:
- Linux x86, x86-64
Supported Web Servers:
- Apache 1.3.x
- Apache 2.0.x
- Apache 2.2.x
- Nginx (starting from Magento 1.7 Community and 1.12 Enterprise versions)
Supported Browsers:
- Microsoft Internet Explorer 7 and above
- Mozilla Firefox 3.5 and above
- Apple Safari 5 and above on Mac only
- Google Chrome 7 and above
- Adobe Flash browser plug-in should be installed
PHP Compatibility:
- 5.2.13 – 5.3.15
- Required extensions:
  - PDO_MySQL
  - simplexml
  - mcrypt
  - hash
  - GD
  - DOM
  - iconv
  - curl
  - SOAP (if Webservices API is to be used)
- Safe_mode off
- Memory_limit no less than 256Mb (preferably 512)
MySQL:
- EE 1.13.0.0 or later: MySQL 5.0.2 or newer
- EE 1.12.0.2 or earlier: MySQL 4.1.20 or newer
- CE (all versions): MySQL 4.1.20 or newer
Redis NoSQL (optional for CE 1.8 and later, EE 1.13 and later)
- redis-server version 2.6.9 or later
- phpredis version 2.2.2 or later
SSL:
- If HTTPS is used to work in the admin, SSL certificate should be valid. Self-signed SSL certificates are not supported
Server – hosting – setup:
- Ability to run scheduled jobs (crontab) with PHP 5
- Ability to override options in .htaccess files

And the last question is how do you know your server/hosting meet these requirements or not?

There is a very simple way to check with this article tips How do I know if my hosting compatible with Magento?