Why Doctor Rub Someone's Arm before Injecting a Syringe?
It's isopropyl alcohol applied with some sort of cotton swab. They do this to kill any germs that might be on your skin and could infect the injection site.
When injecting into a vein, rubbing or patting stimulates blood flow to that area and makes the vessels consequently larger and easier to spot as they expand and bulge against the skin.