In Joomla 3, once you enable Search Engine Friendly URLs (obviously for better Search Engine Optimization), you will probably get index.php in your address.
Something like

If you want to remove the index.php, it is very simple. Besides enabling the Search Engine Friendly URLs, you’ll also need to enable URL rewriting.

Quick Steps:

1. Go to Global Configuration
2. Enable Search Engine Friendly URLs
3. Enable URL rewriting

Note: If you want more SEO benefits it would be a good idea to install Joomla components for SEO