In this sentence it means your legs are very well. To say something is dandy, or fine and dandy is a corny old expression that no one uses these days. If you say this to a native speaker it will sound a little odd and almost gay. (At least in America). I laughed when I read the sentence because it's such a corny expression. So my advice is don't use it.

Millions of North Americans use it. The newest generation generally doesn't use it at all. But many people over the age of 40 use it and almost everybody knows what it means fine, good, well etc. It is used to express these things but it is also used sarcastically. Where I'm from in Canada we use it more for sarcasm than any other meaning.

Dandy comes from Dandelions (a type of flowers) - during the English Middle Ages dandelions were a symbol of prosperity, therefore, if you are legs are fine and dandy means that they are good...they feel fine... maybe you can say that after a marathon or working out...