Operating agreement
The private contract among an LLC's members setting out ownership, profit splits, management and what happens when members leave.
Think of the operating agreement as the LLC's house rules, written down and signed. It says who owns how much and how profit and losses get divided. It also says who decides things, how someone new comes in as a member, and what happens when a member quits, dies or just wants to sell. Two or three members who fall out will go straight to it. A one-member LLC can get by with a few pages, and those pages help show the business is kept apart from the owner.
Most states never see it. It sits in the company records. New York is one of the few that insist: Section 417 of its LLC Law says members "shall adopt a written operating agreement", and allows it before, at the time of, or within 90 days after filing the articles of organization.
Electing S corp status? Read the agreement again first. The Form 2553 instructions require one class of stock. In practice that means every member gets identical rights to distributions and liquidation proceeds, in proportion to their shares, and the agreement should say so.