You can see in the photograph how all of the flowers have been deadheaded from the branch on the right and there are only seed pods left. The branch on the left has many new buds getting ready to open. At the point marked with "Next" is where the next branch will emerge when the new branch has produced most of its flowers. Most cultivars will produce 3-5 branches before the stem becomes exhausted.
If the exhausted branches are not removed then the plant will waste valuable nutrition growing seed pods and the extra flowering branches will not develop. However, eventually the stem will stop throwing branches, at which time the whole stem should be cut off just above ground level so that the new emerging stems do not have to compete for light and nutrients and also improve the air flow around the lower stems. In addition, the foliage on the old stem will start to look jaded and the appearance of the whole plant is improved by the stem pruning.