The Rohan design symbolises the culture and iconography of the Rohirrim, as described in The Lord of the Rings - proud people with a strong monarchy, known for their skilled cavalry and horse training.
"I have been among them," [said] Aragorn. "They are proud and wilful, but they are true-hearted, generous in thought and deed."
The design took inspiration from tapestries depicting historical tales which were said to line the halls of Meduseld (the Hall of the King of Rohan), as well as descriptions of the banner of Rohan and Théoden's shield.
The pattern contains Celtic knot-work, interlocking shield-like formations, which reference the proud warrior tradition of the Rohirrim, as well as sun & star emblems and a rearing horse icon as we might imagine their banner to contain.