To understand this, we think it is best to go for a walk in the woods. What is underfoot? A covering of composting vegetation, scrape this and the most wonderful organic compost/soil exists. Even the least green fingered person appreciates the majesty of this soil.
Now walk down a street, what is around the trees in the pavement, tarmac, slabs, resin bonded gravel, bonded gravel, in grass verges, perhaps a tiny bit of soil, rarely a very small area of mulch?
Mulch, preferable with leaves, but woodchips are usually more appropriate, this increases Mycorrhizal activity ( http://www.rootgrow.co.uk/mycorrhizal-fungi.html ). Mulch increases Mycorrhizal activity by upto 15 times over grass. Mulch as it composts adds organic matter to the soil, improving it's health.
If you are wymiscally minded, when you go on holiday or if you move abroad, you bring items home, from images to trinklets, to remind you of home. That is what trees feel with mulch, it reminds them of home! The woodland floor or the time before humans started removing leaves.
Mulch is incredibly beneficial to the roots and quality of the soil around trees. It should be installed 3" deep and it is vital to keep the immediate area around the trunk clear (it is meant to be above ground and raising mulch up the trunk is as bad as heaping soil up the trunk). How far should it be spread? As far as the roots spread!
It is not a one off application, to maintain benefits it should be regularly topped up. In addition to deterring weeds and grass maintenance machinery (strimmers damaging bark kills many trees), it adds organic material to the soil (soil is a living organism and needs to be fed, the soil feeds the roots (it's not quite as simple as that, but it essentially this) and it retains moisture in the soil. Most importantly it helps Mycorrhizal fungi.