Yankee Doodle went to town,
A'riding on a pony,
Stuck a feather in his cap
And called it macaroni.
Some definitions might help:
Yankee: 18th century term for a United States native
Doodle: 17th century slang for a "fool"
Macaroni: 18th century term for vanity or obsession with one's appearance
It's kind of odd actually that it became a popular patriotic song here because it's likely that it was originally sung by Britons making fun of Americans during the French and Indian War! This verse is basically saying, "These American fools think that by sticking a feather in their cap, they are being fashionable!"
Maybe it would have been better to have just believed that Mr. Doodle called his hat a tubed piece of pasta! :)