iCloud tab syncing is a deceptively simple but powerful feature that integrates the browsing experience across multiple devices. Any iPhone, iPad or iPod touch running iOS 6 and any Mac running OS X Mountain Lion will, if connected to the internet and your iCloud account, sync any open tabs across all of your devices. iCloud Tab syncing between Macs has been possible since Mountain Lion's debut; iOS 6 brings this feature to Apple's handheld devices.
This means the days of emailing links between devices or simply trying to remember what that one website was you were viewing on your iPad in the bathroom when you're sitting at your Mac in the living room are now over. Any tabs open on any device can be viewed on any other device.
This does of course raise some red flags if you prefer to keep your browsing as private as possible. With a little patience, anyone with access to one of your devices could easily see what you're up to in your browsing session on another computer. Enabling Private Browsing on any device stops its Safari tabs from syncing as long as Private Browsing is enabled. You can also disable iCloud tab syncing altogether by turning off Safari syncing in Settings.
On the iPhone, while using Mobile Safari in landscape mode you can toggle a fullscreen mode via a touch control in the lower right of the screen. Once toggled, the URL/search bar at the top and the toolbar at the bottom will slide aside, presenting far more actual content on the screen. Simple hover buttons for forward/back will still show up, as will the fullscreen toggle.
As far as new features go for Safari in iOS 6, that's basically it. Reading List has a new offline reading mode similar to what Instapaper's offered for years, Safari gets the same simplified sharing button interface that's in the rest of iOS, and switching between Bookmarks, History, and Reading List is slightly easier on the iPad now thanks to a minor interface tweak.
Safari in iOS 6 still doesn't feel like it takes full advantage of the capabilities of the devices' multitouch screens. It seems strange that multitouch gestures I take for granted on the Mac, like two-finger swipes to go forward/back or pinching out to see a tab switcher, don't work on my iPhone or iPad. Maybe I'm in the minority, but I think gestures like those definitely have a place on Apple's touchscreen devices.
Fullscreen mode on the iPhone
Apple iPad Air 2
Apple iPhone 6s