On the Seventh Day of Christmas...

... My true love gave to me 7 swans a swimming, 6 geese-a-laying, 5 golden rings, 4 colly birds, 3 French hens, 2 turtle doves, and a partridge in a pear tree.

In the medieval ages swans were domesticated, and commonly served at Christmas dinner. In England, around this time, swan breeders would mark their swans' beaks by carving a symbol. Any unmarked birds belonged to the British Monarchy. Swans were considered a generous gift from the British Monarchy for Christmas dinner, 7 swans as a gift could be considered much more than generous, maybe even graciously generous :)

For Catholics, the seven swans represent the Seven Sacraments. This interpretation of the song mostly likely developed in the 1700's.

I learned this here.