The First reason is because it gathers everything that concerns you in one place.
You can have your browsing history, your geolocation history, your purchase receipt, your account statements... anything that concerns you and that you could automatically receive from third party. There is also data you produce your like your holiday pictures, your running itinerary and performance...
This is very convenient simply to access it, but the real value lies in letting users total control and freedom in the way they decide to use it.
There is no restriction for the user to access its data, no restrictive API, it's there and ready to be used. Programmers can develop their own tools to do quantified-self for instande and mashup any data they want. Also applications can develop like for instance, a "travel" app. Everything related to your travel, from pictures, to receipts to persons you met are in your private cloud, and this hypothetical app would be a way to remind a journey differently. Because everything run in your personal place you control, there is no need to communicate your data in many case hence the bonus for privacy.
That doesn't mean you isolate yourself from companies, data disclosure project aims to give users a way to correct information companies hold on the user, to update their information in one place, and to let them remove information they don't want. More trust is good for business. Users could decide to share more data with companies and receive discounts, or directly give feedback on the product.
Ultimately it is all about giving users the same tools that companies have to deal with the relationship. It brings more transparency and control over privacy.
If I sparked your curiosity, I highly recommend you reading about project VRM by Doc Searls, and visiting the Personal Data Ecosystem Consortum. All this could seem crazy right know but this is really happening pushed by government's Data disclosure projects. The U.K. already made compulsory for some industry(energy, telecommunication..) to disclose personal data to empower users.