A good dill pickle (a pickled cumcumber) should be firm and crisp. The lady in the commercial is a "pickle lover" (an aficionado of pickles) and was disappointed when she bit into the pickle and it was soggy and flavorless. She expressed her displeasure by destroying the room. The end line, "If you were a pickle, wouldn't you want to be....") is just a joke. It's asking if you wouldn't want to be the best available. It's the same as asking, "If you were a car, wouldn't you want to be a Rolls Royce?"
(Here's how a nice crispy pickle should look. )