It is a polite way of saying that what was said i a letter/email was sincere and honest.

In the US, at least, it is common to write this after the main text or body of a letter above one's signature. This is usually used in semi-formal and formal situations. Personally, I would write, "sincerely yours" or just "sincerely". In some situations, one could also write "yours truly". When I worked at an Ice Arena, I once looked at the company's letterhead that they send to their customers. They concluded with, "yours in Hockey". "Yours" kind of means that the person receiving the letter is in possession of the sender. Or, at least that he or she possesses the sender's sincerity. Of course we do not actually think that one person owns another but this is sort of the idea. Technically, I think "your" is a possessive adjective. Therefore "yours" is a variation on it. Maybe "yours" is used more when the noun being described is not actually stated. This is your car now. = This car is now yours. = This car belongs to you now.

Yours is short for Yours sincerely or some people write Sincerely or Sincerely yours