Girdling

If bark is removed all the way around a tree trunk the downward passage of food to the roots is stopped. Eventually the tree will die (Ok if that is what you planned).
This Girdling can happen when rabbits or deer eat the bark in winter.
Girdling can also be caused by mechanical damage like an aggresive strimmer or cultivator.
This Girdling damage can sometimes be repaired by bridge grafting.

Girdling has another meaning in USA where it also refers to the cutting of roots to prevent them from encircling the trunk and stiffling growth.
It can happen when a tree is too close to a wall or on street trees where buildings interfere.
The offending roots need to be cut and removed.

Garrotting

This is a method of deliberately restricting the growth and is often used to encourage a fruit tree to increase fruiting.
It is carried out by tying wire or metal around a branch or trunk and twisting it like a tourniquet.
This restricts the movement of sap and redistributes natural hormones made in various parts of the tree.
The effect is similar to ringing but less dramatic and lasts fewer seasons.

Ringing

This is another method to encourage fruit tree to crop better.
It works by severing or partially severing the flow of food materials and hormones that naturally pass down the tree.
A ring of bark upto quarter of and inch wide can be stripped away in April or May.
A half ring may be safer and should be tried first.
Knife ringing is done on an individual branch. No bark is removed but a knife cuts through the bark all the way around.

Nicking and Notching

The removal of a crescent of bark above a dormant bud or ‘nicking’ is often used to stimulate a fruit tree bud into growth.
A similar operation below a bud is called notching and both techniques are used to encourage the right buds to grow and the wrong or notched ones to be deprived of sap and hormones.

Explanation of Plant Food and Water Transportation
http://youtu.be/oVFRPRZDxyE