It promotes the idea that the most important employees are those who deal daily with the organisations' customers, ie those who would normally be at the 'bottom' of the hierarchy. It is then the role of supervisors and managers (normally 'higher' in the hierarchy) to support these employees and to remove the obstacles that hinder them in satisfying their customers' needs. Thus the 'more senior' people are actually 'lower' in the inverted pyramid, as they have more people to support.
Some organisations claim to be operating in this way when in fact all that has happened is that the organisation chart has been drawn in an inverted fashion.