サービス means "goods or services free of charge", "something that is done as a special service to customers", "free gifts", "special offers", and so on. It's not DIRECTLY related to the English word "service".
So the sentence means something like "Right now, they have special/free offers (サービス) during the period (期間中) of commemoration/celebration (記念) of their 10th anniversary (10周年). Everybody, let's go!" (and grab some of this free stuff before it's gone...).