In this context Yours means your letter, i.e., the letter you sent.
to hand means: within reach, accessible, at hand.
at hand means: within easy reach; near; close by
So the meaning would be:
- "I have received your letter and in reply to it..." ; or
- "I have your letter right here beside me (to hand, at hand), and in reply. . ."; or
- "I have your letter in hand, and I'm replying."
If you have information about the origins of the phrase, please share them as comments. Thanks.