Well, a bit of research quickly found some history. The idea started with the New Jersey Council of Garden Clubs in 1944 when 8,000 dogwoods were planted along US 22 to honor members of the armed services in World War II. A blue star banner or flag can be used to designate residences where a family member is serving during a conflict. That 5.5 mile stretch of highway was designated "Blue Star Drive" by the state legislature in January 1945.
Later in 1945 the National Council of State Garden Clubs adopted the program and began extending it nationwide. The program is continued today by that organization under its present name, National Garden Clubs, Inc; details are here. Two other types of markers have been developed in recent years.
Alabama has a number of them; a state-by-state listing up to May 2015 is here. From what I could determine from that list, this particular marker was dedicated on August 27, 1990.
The "Blue Star Memorial Highway" now extends over 70,000 miles in 39 states.