Apache modules are extensions to your webserver's capabilities. For example, mod_rewrite will make "pretty urls" in Magento work, mod_deflate will facilitate compression of assets and mod_php (depending on your set up) will run your PHP code for you.
The installation and activation of these modules is dependent on your hosting platform, but in general, it involves changing the Apache configuration file load the appropriate modules (see http://httpd.apache.org/docs/2.2/mod/ for a full list for Apache 2.2).
If you happen to be running Ubuntu server as your OS, there is a nice and easy helper utility available to enable Apache modules. You will need root access to your server; if you do, log in via SSH and run:
Where <module-name> is one of the supported modules from the list above. After that, you will need to restart Apache, which on Ubuntu, you can do by running (as root):
Hopefully that is of some use to you!