I always think of the Gestalt principles when laying out content - whitespace helps apply these principles by emphasising association, grouping, separation, alignment, similarity and symmetry.
Without the whitespace you cannot apply these principles because the whole becomes a homogenous chunk instead. Only with the whitespace can you end up being able to distinguish figure and ground; relate in your own mind what the page is made up of and decide what is important (by scanning the content first) and what the relationships are between regions of content.
Web Design Tuts has a great page with example on the importance of whitespace. The links work if some of the images don't. It talks about white space in design including text and images.
-- update --
From a higher level perspective, it's very easy to add information to a website. It's much harder to add the gaps.
Adding gaps doesn't necessarily mean literally inserting a gap between one part of the content and another. It's about considering whether each part of the content is relevant in the view, and removing those elements which are not necessary.
But every part of the content will have been provided by someone who feels that it is important - or at least no less important than someone else's bit of content which is vying for position on a home page for example.
Thus we get into the interests and impacts of business rules and business analysts, content strategists, domain experts, copywriters and the like.
So you can see how it starts to get difficult to decide what not to include on any given page. The more elements there are, the more the user has to digest and think about - and the more decisions the user has to make. If you make that top level information easy to digest, the easier the user will find it to navigate in the right direction.
Deciding what not to include is what takes the time and effort.