Your default browser on the Nokia Lumia Icon is going to be Internet Explorer. The name has left a bad taste in everyone's mouths, but for your purposes on the Lumia Icon, it does just fine.
The URL bar down below also doubles as a search bar for Bing search. You can also search by voice, but oddly the option doesn't pop up in the bar until you've already begun your search. Alternatively, you can always use the long-press feature on the home button to search for things on Bing.
With Internet Explorer, you can do tabbed browsing, and you can even pin web pages to the start screen if you like. Like other mobile browsers, you'll also be able to save pages to favorites or bookmarks for quick access.
There is an option in settings to select a viewing preference for web pages, whether you want mobile or desktop versions. This is great, especially since many sites have mobile versions that aren't as feature-rich as their desktop counterparts.
In short, the browser is very barebones, which is a good thing. It gets the job done without getting in the way, it's simple and easy to use and you'll rarely ever have any issues with it crashing or stalling (unlike the desktop Internet Explorer we've come to know and hate in the last 15 years).
There are a number of ways to access multimedia on the Lumia Icon. One is via the Music + Video app, which is basically a collection or aggregation of the music and video apps you already have on your phone.
If you have Spotify, Netflix and similar apps installed, for example, they'll all fall under the Music + Video app.
From there, you can watch movies and TV or listen to downloaded music or stream music if you've subscribed to a service that allows you to do so.
There is also Nokia MixRadio, which allows you to stream music and download songs for offline listening. You can purchase music here and see more info on the band/artist/song that you're searching.
You'll also be able to connect to Xbox Music, which will give you access to a large music library and options on how you can listen to music. You may be better off subscribing to a music streaming service since they are more cost effective - songs on Xbox Music cost, on average, $1.29 a pop.
You can also record your own videos and other content with Nokia's built-in apps, but we'll get to that in the camera section.