It means that when something/someone [ a product or a person] that has been taken away is given back, because lots of people enjoyed or needed it. Examples: The TV host was back by popular demand The cereal was back by popular demand.

back = has come back; had been brought back popular demand = it is wanted by a large number of people Because a lot of people have demanded it so, the song has come back onto the market. The song is back by popular demand.