frighten his brother into fits
"Bill Starkey," continued John, "did not mean to frighten his brother into fits when he
dressed up like a ghost and ran after him in the moonlight; but he did;"
This quote is from Sewell's 'Black Beauty'. It talks about ignorance and mischievous acts. But the usage of "frighten his brother into fits" is a bit vague to me. Could you explain it in some detail? What is the relation between the meaning, which I guess is that he scared him, and the words used in that idiom or expression?