New York City is the world center of Kosher dill pickles. Kosher originally meant the pickles were manufactured and certified in accordance with Jewish dietary rules, but these day not all Kosher dill pickles are necessarily Kosher. It usually means that the pickles are made in the traditional manner of Jewish New York City pickle makers--a particular form of salt brine with generous amounts of garlic and dill. I think the jar above might actually be real Kosher.
I could hop up and run in the kitchen and check the label again and see if it is certified Kosher but I am too lazy. In this part of Brooklyn they are very likely to be certified Kosher. Alex eats 3/4 of the pickles in this house and he does not require Kosher.