You can read what the official WSSNDL by-laws say about the duties of the Executive Board here [Sec. II. D.]. Below you'll find a touch more insight than just what the bare minimum job is. Members serve one-year terms (two playing seasons), and there are no term limits.
The President mostly puts out fires, but also rules on interpretation of league rules, makes decisions for the League with consultation with the Executive Board, settles complaints, conflicts, and issues, schedules and conducts League and executive meetings, and serves as liaison with our playing venues. Beyond that, the President is responsible for the overall health and thriving of the League, promoting the WSSNDL, recruiting and placing new players & teams, recruiting new venues as needed, maintaining a good image for the League, and guiding all League activities both within the season and outside—like the Annual Brian Lee Tournament, the Summer Season, and cooperation with other darts events and organizations in the interest of the WSSNDL. Over the past 7 years, the President has also managed and designed the website.
The Secretary/Treasurer is two jobs in one person. This exec member tracks, maintains, and collects dues from team captains as well as from our host venues. This person maintains and manages the League checking account, and handles all financial transactions for the League—catering for the banquet, charitable donations, website costs, awards, etc.—and produces financial statements for end-of-season meetings. This dual-role also takes and posts minutes for meetings, crafts meeting agenda in consultation with the President, organizes the banquet and its catering, and orders and acquires end-of-season awards. The Secretary/Treasurer also assists the President as a liaison to venues.
The Statistician prepares each season's schedule in advance of the first captains' meeting, taking into account the changing number of teams from season to season, the number of available venues, holidays, the number of weeks available, etc. This person also collects weekly match score sheets and interprets bad handwriting and incomplete or conflicting information. The Statistician then tabulates statistics like team and individual Win/Loss records, QPs, player ratings, and standings. He or she posts weekly updates of the season statistics, schedule, and standings to the website. Per the League Rules, the Statistician maintains the website as well. The Statistician also prepares the list of award winners at the end of each season so the Secretary/Treasurer can procure awards for the banquet.
The Vice Presidents are members, one representing each division—Winston and Salem, if the League is organized into two divisions that season—who act in the absence of the President and serve as representatives of their respective divisions to the Executive Board, weighing in on decisions, disputes, and issues. The Vice Presidents would also preside if there is a dispute involving the President.