Give way; give in; submit.
In the 18th century, 'knuckle down' was used used to mean 'acknowledge oneself beaten; submit to another's authority'. The word 'knuckle' by itself had the same meaning. 'Knuckle under' was later coined in the USA, also with the same meaning.
Dyche and Pardon, in their A dictionary of all the words commonly us'd in the English tongue, 1740, defined 'knuckle' like this:
"Knuckle or knuckle down: to stoop, bend, yield, comply with, or submit to."
The allusion appeared to be with the subservient gesture of stooping with one's knuckles low down or on the ground. While 'knuckle down' is now commonly used with a different meaning, 'knuckle under' has persisted.
The first reference that I can find to the term in print is this jingoistic piece from The New-York Weekly Tribune, June 1852:
"Will anybody admit that an American citizen, with plenty of money in his pocket, is not as much of a man as anybody else? Is it for him to knuckle under to the bedizened aristocracy and soldiery of Europe? No, 'Sir!"