The gland of a female mammal in which the milk is secreted and stored for the nourishment of the young;- commonly called the bag in cows and other quadrupeds. — Webster, 1882
Almanzo had finished milking, he filled the pans for the cats. His father went into Blossom’s stall with his own pail and stool, and sat down to strip the last, richest drops of milk from Blossom’s udder. But Almanzo had got it all. – Farmer Boy
All those Little House books, and the word udder is only mentioned once, in connection with Father Wilder checking to make sure Almanzo was a competent milker in Farmer Boy (he was). The udder of female cattle is the bag-like organ containing multiple mammary glands, each with its own nipple.
udder (FB 2), see also cattle / cow / calf