Most apples have a food grade shellac on the peel to keep them fresh. I'm guessing you probably don't want to eat this, plus the caramel will have a harder time sticking if it's left on. To remove, soak the apples in a sink of water plus a few tablespoons of vinegar for 15 minutes. Rinse and dry thoroughly with a clean tea towel.
To make the caramel, melt the butter in a heavy saucepan on medium high heat. Stir in the brown sugar and reduce heat to medium, stirring frequently until the sugar is dissolved and the butter is incorporated. Add the maple syrup, and mix thoroughly. Finally, add the sweetened condensed milk, and return to medium high heat. Bring to a boil, then cook, stirring constantly, until the mixture reaches 235°F (use a candy thermometer for best results). Remove from heat and stir in vanilla.