The solid blob on the end of each arm of the Pommee Cross represents an apple, and apples represent the fruits and rewards of living a good Christian life.1
In the Bible2 the apple is always referred to as a treasured item; either as a sweet-smelling fruit, or referring to the apple tree giving shade for a tent or house. It also uses the term apple of one's eye. The eye's pupil used to be called an apple because of its round shape. So the apple of one's eye was at first a literal phrase describing the pupil. Because sight was so precious, someone who was called this as an endearment was similarly precious.
Contrary to popular belief, there is no mention in the Bible that the fruit in the Garden of Eden was an apple. In Genesis we read that the forbidden fruit was from "the tree of the knowledge of good and evil"3, which is generally understood to mean that as God created man in his own image4, and so man was pure and didn't know anything about evil. Having eaten from this tree, Adam and Eve then knew the existence of evil, and at this point they showed their fear and shame5.
God had given them a choice, just as we have today, to choose between good and evil. True love doesn't force one to love another; there is the choice.
Why this reference to a tree? Well, choices between good and evil can be represented schematically like the fork of a tree branch. When we make a choice to do good or evil, we are developing our soul through the branches of this tree. The route we take determines our destiny; heaven or Hell. (See also the Forked Cross)
But back to the Pommee Cross. Ancient Turkish coins were called Bezants from the city's earlier Greek name, Byzantium (see also Byzantine Cross). These gold coins had a wide circulation throughout Europe in the Middle Ages. It is supposed that English crusaders returned with such gold coins and the symbol then became part of English heraldry resulting in the name: Bezant Cross (or Bezanty Cross).
The French have been great creators of heraldic designs, and the bezant can be likened to an apple of gold1. Apple in French is pomme, hence Pommee Cross with various spellings including Pometty (French: Pommettée) and Pomy. Also known as Croix Bourdonnée, using a heraldic term for something which terminates with a roundle, such as the end of a swordhilt.