As much as modern desktop web browsers can do, their basic concept is stuck in a rut. It's not really designed for the way many people use the web, such as chatting while you surf. Opera wants to climb out of that hole, and it's trying an unusual approach to make that happen: it's launching Opera Neon, a separate "concept" browser that shows where software could go. It's much more visual, with an uncluttered look, tabs and shortcuts as bubbles and a side control bar that largely gets out of your way. However, the real fun starts when you want to juggle multiple sites -- this is more of an intelligent desktop than your usual web client.
If you want to have two pages running side by side, it's relatively easy: you drag one of your open tabs to the top of the window, creating a split view much like what you see in Windows or the multi-window modes on mobile devices. Also, Neon acknowledges that your browser can frequently double as a media player. You can listen to tunes in the background, or pop out a video in order to switch websites while you watch. These aren't completely novel concepts all by themselves, but it's rare to see all of them in a browser at the same time.
There are two more perks that you might appreciate if you're a power user. A smart tab system surfaces frequently used tabs, while a quick "snap" feature captures screenshots of websites for a gallery. If you're the sort who regularly wants to share photos and quotes in chat, this might be your pick.
Neon is available now for both Mac and Windows users. Don't expect it to replace the standard Opera browser, though. Some of its features should cross over in the spring, but this is really a separate experiment to see which ideas stick. You'll most likely want to give this a try if you either do a lot of web-based multitasking or just feel that your existing browser choices are a bit stale.