A. There’s no religious significance to the pickle, but you’re right, along with herring, pickles and other pickled products have an important place in our cultural tradition (at least for Jews with Eastern European heritage). Back then in cold countries you needed ways to preserve foods during the harsh winters, and pickling was a practiced method to do keep these foods edible over long periods of time. And don’t forget, Jews would say a little L’chaim on some vodka or schnaps on Shabbat and festive occasions, and these foods are good chasers. But there is also a life-lesson from pickled and spicy foods as explained in the Chassidic classic book of Tanya chapter 27, for they represent (in contrast to sweet foods) the challenges and difficulties we have to overcome in life. When we grow through the difficult experience, it is a far greater enjoyment than the satisfaction in that which comes easy.
See this post on Tanya 27’s sweet or savory for more on this issue. And you might also enjoy our post on two types of pickles for a different Jewish pickle message.