Tree branches should always be pruned back to the branch collar.
The branch collar is the area of tissue around the base of the branch. It is usually identified by a distinct collar of built up wood around the branch base. Some tree species have more distinct collars than others.
The branch collar provides a physical and chemical boundary between the branch and the trunk which stops the spread of decay into the main trunk of a tree if a branch breaks off. Removal of this boundary opens the tree up to decay causing organisms which can be detrimental to tree health and human safety. See image below.
When pruning your tree, ensure that you always cut back to the collar and do not leave stubs. Dying branch stubs are also a food source for decay causing organisms. They are unsightly as well.
Correct pruning techniques require the correct tools. Secateurs or loppers will need to be used on smaller trees and shrubs, while a hand saw or powered chainsaw will be required for larger limbs. Always ensure than a slight under cut is made on larger branches. This will stop the bark from peeling down through the all important branch collar. See image below.