Large bruises on the arms after blood donation are the result of localised bleeding. There are several main causes.
Firstly, the needles used to draw blood were thick and damaged the local blood vessels significantly.
Two, the needling site is not well pressed, damaging the vessel wall causing blood to flow out and pool under the skin, which can be accompanied by local pain.
The third is caused by abnormal blood clotting and failure to stop bleeding for a short period of time.