The Roman salute is a gesture in which the arm is fully extended, facing forward, with palm down and fingers touching. In some versions, the arm is raised upward at an angle; in others, it is held out parallel to the ground.
The politically correct view now is that Jacques-Louis David's painting The Oath of the Horatii (1784) wrongly created the impression that it was used in Ancient Rome. Regardless, it was earlier widely believed to have been used in Ancient Rome and therefore used by Italian fascists and later by other fascists (broad sense) more generally, including by National Socialists.
After WWII, similar to the swastika and some other National Socialist symbols, it is now in some Western countries either completely outlawed or considered to be an expression of anti-Semitism and/or racism and publicly displaying it may cause the user to be affected by various hate speech and hate crime laws.