"My honor is loyalty" means:
Our loyalty is honor.
The famous saying of the SS in German is Meine Ehreheiβt Treue
It is the slogan of the German Nazi SS Viking Division. It seems to be embroidered on the military flag. German soldiers must take an oath when they join the army. Before Hitler came to power, he swore loyalty to the country. After Hitler came to power, the country = nation = head of state!
Such slogans can be traced back to the oath of allegiance of knights in the Middle Ages. After the Nazis came to power, there were many "retro" behaviors to express the inheritance of "excellent history."
Swearing loyalty in the SS is to declare that the army is loyal to the "Führer" (just like the ancient knights swore loyalty to the king). It is Hitler's method of controlling the army (the Wehrmacht does not say this, the Wehrmacht Loyal to the "country" rather than to individuals or parties. That's why Hitler was always worried about the Wehrmacht).
The practical significance is that soldiers must maintain a high degree of loyalty to their leader, resolutely obey the orders of their superiors, and not betray their leader.