Reducing the crown is making the tree smaller without spoiling the shape. This is very skilled work as each branch must be cut specifically to the right growth point at exactly the right point to keep the tree symmetrically balanced and again it is done to reduce the size/weight in potentially dangerous trees, but it can also be useful if trees are obstructing objects. Crown thinning is the selective removal of the inner branches evenly throughout the entire trees crown allowing more light to travel through, this also lets air circulate more effectively throughout the canopy reducing wind resistance making the tree less liable to storm damage without altering the trees natural shape.
