It costs money to keep our jobs, good jobs. Membership dues allow unions to employ staff members, pay for a meeting space (the union hall), conduct member training, etc.
Your dues are at work when you see a union staffer representing a member in a grievance meeting; when they are educating members in employee cafeterias; building area standards through negotiating new contracts; organizing new properties; building community support for our union; getting our message out to the public through various media outlets; paying for lawyers to defend our rights; organizing rallies; etc.