To slobber is to allow spit, or saliva, to drip from your mouth. Your dog will probably slobber if you tease her with your hamburger.
Another word for slobber is drool. You can use it as a verb, as in "That cupcake made me slobber," or a noun: "Wipe that slobber off your chin." To figuratively slobber over something or someone is to be overly enthusiastic or sentimental, like when your friends all slobber over your adorable new puppy.