A "posy" is a small bouquet. The word "posy" is still used today. You hear it most associated with the small bouquets flower girls carry at weddings.

Posy is a very, very old fashioned way of saying bouquet. You probably would have heard it more in the 1800's. I've only heard it in children's rhymes.

I agree with Magenta. A posy is a small bunch of flowers tied together (usually prettily) that you can hold in your hand. A bouquet is a much larger flower arrangement.