Moonshine is a type of alcoholic beverage illegally produced. A moonshiner is someone that makes moonshine. The person in the joke is saying that they "still" love the moonshiner's daughter. The word "still" can be seen in "distilled".  A "distilled beverage" is an alcoholic beverage. This joke is playing on the word "still". 
She was only a Moonshiner ' s daughter , but I love her still .