Swipe keyboards, pioneered on mobile devices by Swype and widely available on Android devices, are a popular alternative to the standard keyboard. Rather than tapping each letter one-by-one to enter a word, swipe keyboards use a single finger trace gesture (line) drawn from letter to letter (i.e. w-o-r-l-d).
Software built into the swipe keyboard is intelligent enough to work out near misses and double letters / meanings (e.g. swipe h-e-l-o and the keyboard will assume, depending on the context, that you mean "hello", based on word frequency / popularity). There are also specific gestures for punctuation and other keyboard shortcuts.
The key advantage of a swipe keyboard is that it potentially allows for faster text entry. The exact speed, and whether it is faster than the standard keyboard, depends on the amount of familiarity with the respective systems and individual preferences. Some users also find it a more comfortable way of entering text one handed.
From the video it appears that the Windows Phone swipe keyboard uses the same layout as the standard keyboard and has similar smart prediction / correction capabilities. These are likely to be tweaked for the mistakes that more commonly occur when using a swipe keyboard (certain mistakes are more likely to occur when using a swipe keyboard). The swipe entry is shown as a disappearing blue line overlaid on the main keyboard.
It is likely that the keyboard will be an optional extra to the standard keyboard and that both standard and swipe entry will be able to be used on the same keyboard. It is possible that the swipe keyboard may only be available for a limited number of the languages that Windows Phone supports. This is because a swipe keyboard needs a word frequency database in order to be accurate (i.e. correct near misses and traces that may be one or more words).