Original: Yours sincerely is typically employed in British English when the recipient is addressed by name and is known to the sender to some degree, whereas Yours faithfully is used when the recipient is not known by name (i.e. the recipient is addressed by a phrase such as "Dear Sir/Madam").
Simplified: Yours faithfully Yours faithfully is used when the person who is receiving the letter is not known by name (i.e. the recipient is addressed by a phrase such as "Dear Sir/Madam").