Yours faithfully›written at the end of a formal letter that begins 'Dear sir' or 'Dear madam', before signing your name: I look forward to hearing from you. Yours faithfully, Jane Brown.
Yours sincerely›written at the end of a less formal letter that begins with the name of the person you are writing to, before signing your name: I look forward to hearing from you. Yours sincerely, Jane Brown.