Hi Olive, If someone 'swears by' something is means they really believe in it, or that it works. For example, I love running in the morning because it's healthy - I swear but it. Or, I like to add sugar to my coffee because it tastes better sweet, so I swear by sugar "it". English is confusing, I know. But, in the end, to 'swear by something' just means you really believe it and want others to know so. Take care, Olive. :)

It means a person attests to a statement or thing such as an item purchased or a testimony given. "She swears by the new self driving car from Tesla." "He swears by his statement as the truth, the whole truth and nothing but the truth."