The interface is designed as a treemap with sections sized in proportion to their annual budget. I can't see any legend that explains the colour coding so assume they are arbitrary. I always aspire to squeeze out as much information encoding from all visual properties as possible so these could have been deployed to communicate something like the expected severity of cuts based on rumour, leaks or fact. Its only a small quibble though, I appreciate this information may not have been easy to get acquire accurately and, in defence of the colours used, they do at least brighten up the prospect of this appalling process!
Clicking on a given department's shape leads you to an option to either reduce the budget by a flat % rate or alternatively select some specific individual large scale projects or budget categories to cancel. Each change you make fills the department's budget segment with an increasing 'waterline' of savings and the aggregate total is displayed at the bottom for comparison with the set target.
You can find a great breakdown of the unfortunate task (or ideology-driven opportunity, depending on your particular political persuasion!) facing the Government here.