Im just relaying info from ArmyFags. Wikipedia says "Shoulder sleeve insignia worn on the upper right sleeve of Army uniforms denote former wartime service." Which is what the ArmyFags said. But it is Wiki so it could be wrong.

https://en.wikipedia.org/wiki/Shoulder_sleeve_insignia_(United_States_Army)

Also from Wiki:

The SSI is typically worn on the left upper arm, just below the uniform's shoulder seam on all but the ACU. The most common place for the SSI to be worn on the ACU is on the upper sleeve, attached using a velcro backing, however it is also sometimes worn on other places, notably when the soldier's body armor covers the shoulders, such as the shoulder pads of interceptor body armor, which covers the upper arm. Some units (such as the 3rd Infantry Division) also wear SSIs on their helmets. SSI are also occasionally worn on the backpacks or rucksacks of soldiers, but this is not standard practice and is usually personal preference.

Which SSI is worn depends on the chain of command that the soldier's formation is a part of. Usually, the soldier wears the SSI of their division or separate brigade, but if they fall under the command of a different division, they must wear the SSI of that division. The First Army has directed that all subordinate brigades wear the First Army SSI instead of their own authorized brigade SSI.

Those soldiers who are combat veterans are authorized permanent wear of the SSI of the unit they fought with on their right shoulder. This shoulder sleeve insignia recognizes "former wartime service" and is frequently called a "combat patch". Per Army Regulation 670-1, a soldier is authorized to wear the SSI of their higher headquarters. This is not dependent on whether or not the higher headquarters deployed, or to whom the soldier was attached throughout his/her deployment.[3] Exceptions have been made for operations of relatively short duration such as service in the Dominican Republic, Panama and Grenada.