It is an orphanage in Nebraska, founded in 1921. It has since expanded to many other locations in the U.S. Starting at least as far back as the late 1940s, the orphanage used Christmas seals to raise funds. They showed a boy carrying another, smaller child, and bore the legend, "He Ain't Heavy Father He's M' Brother." These were ubiquitous on Christmas cards for decades. Here is a picture of the seals.
The meaning is exactly what Matching Mole has described.