Apple have opened a new store on 4th Street, Berkeley CA, and it's a very fine example of design excellence and beauty.
The paving stones outside the store have been used as the ‘master size’. All dimensions have then been taken from this size, e.g. the window sizes are a multiple of the size of the paving slabs. This produces a very pleasing end result because everything is working in harmony. Pedestrians don't necessarily understand why the store is so pleasing to the eye, they just see that it is.
This is the same with layouts. Designers use grid systems and various different proven ratios of beauty to give their layouts the most pleasing look-and-feel. Again, the end user doesn't necessarily know why they like the layout but they know that they do.
Beauty is not the only reason why we use grid systems in our layouts, though. A major added benefit to basing designs on systematic grids is that the human brain finds it easier to remember information which is laid out logically and with clear hierarchy. That's why newspapers are so strict with their layouts. Check out the printed version of the Guardian newspaper for a another great example of this.