By default, you will have Midori web browser as the default web browsing application on Elementary OS Freya 0.3.2. To me, this web browser is not suitable for my browsing and internet activity style. I need something powerful, more features and Midori is not designed for that. So, I choose Firefox to replace Midori.
The most recent version of Mozilla Firefox 43.0 is available on Elementary OS Freya repository. So, installing Firefox 43.0 is very very easy. The easiest way is using Software Center. Open Software Center and type firefox on the search bar. Click Install to install Firefox.
Alternatively, use the following command to install Firefox
sudo apt-get install firefox