For those of you that are not familiar with Ubuntu, it's one of the more popular Linux distributions, available for desktops and servers (with versions compiled for a variety of different processor types, including Intel and ARM platforms).
Ubuntu also announced a phone version of it a while back. It's very unique, in that the User Interface is optimized for a phone when using it with one; yet changes into the full featured Ubuntu Desktop Interface when a larger display and keyboard are attached, optimizing the User Interface for the device it's being used with.
IOW, rather than trying to use the exact same UI on a phone with a smaller display and a desktop with a larger display, the User Interface is being designed to change when it detects the phone is being used as a desktop device instead.
IMO, it's a much better design for use with multiple devices compared to something like the new Windows 8 interface (where users with desktops using larger non touch displays and keyboards are trying to use a [formerly known as Metro] UI that's more optimized for touch displays instead). There are lots of debates about how Microsoft designed it's new style UI. But, in my personal opinion, it's trying to be a "jack of all trades, and a master of none", and it's just a bad idea trying to have the same UI on multiple devices.
Instead, the Ubuntu for Phone UI is designed to change in order to work better for different uses (allowing your phone to work like the standard, full featured Ubuntu desktop when a keyboard and larger display is attached, yet optimized for a touch screen phone with a smaller display when you use the phone by itself).
Given the evolution in phone processing power (newer and faster processors and graphics chipsets, more memory, etc.), that means that we'll see one device that's optimized for all computing needs (your phone, which will have a UI optimized for a smaller touch display when used as a phone, with a User Interface optimized for a desktop when used with a larger display and keyboard).
See this Overview page for more information about Ubuntu for Phones:
Also see the other pages linked to, including the design page, and make sure to watch the Ubuntu Keynote video linked to by Mark Shuttleworth that was published in January 2013. It's a bit long (and most of the first 5 minutes is just a discussion of Ubuntu in general, versus Ubuntu for Phones).
But, you'll see more about the design of Ubuntu for Phones later into that keynote video. I'd probably start the video at around 5 minutes and 20 seconds into it in order to see more about Ubuntu for Phones. Just use this link (and I set the link so that it starts the keynote video at 5 minutes and 19 seconds into it for info specific to Ubuntu for Phones):
Earlier versions of Ubuntu for Phones have been available to developers for a while now, and are optimized to work well on the Google Nexus 4 phone (but, it will work on a wide variety of hardware as it matures). Ubuntu for phones will also be able to use existing Linux Kernels and Drivers that have already been optimized for a wide variety of devices and hardware running Android (keep in mind that Android is using a Linux kernel, so the existing Linux kernels and drivers that work with existing Android devices can also be used with the new Ubuntu Phone OS).
More and more features are being integrated over time, with next month's release of Ubuntu 13.10 having most of the features needed to make a phone work well as a mobile device, and as a full featured Ubuntu desktop when a larger display as attached.
But, all of the features and integration planned probably won't make it in until early 2014, at which time we should start seeing phones including Ubuntu shipping from major carriers.
For example, both Verizon and T-Mobile in the U.S. (as well as a variety of carriers in other regions) are already on the advisory board, and I expect more carriers to follow. Chances are, these phones will be dual boot to start out with (allowing users to choose between either Ubuntu for Phones or Android after each restart).