It covers who owns what percentage, who can make which decisions, how profits are distributed, what happens when someone wants out, how new members are admitted, and how disputes are resolved. Most states do not require one, and if you have none, default state rules apply — rules written for a generic business, not yours, and often not what either party assumed.
The reason to write one is that it is the only document that exists for the bad day. Partnerships end, people's circumstances change, and someone eventually wants to sell, stop working, or be bought out. Deciding those terms while everyone is optimistic costs a few hundred dollars; deciding them mid-dispute costs a business. Single-member LLCs benefit too — the agreement is evidence that the company is a genuine separate entity rather than an alter ego, which matters if anyone ever tries to pierce the liability shield.
A concrete example: two people form an LLC 50/50 to run a small manufacturing business. Two years in, one wants to exit and take a job. With no agreement, there is no valuation method, no buyout mechanism and no tiebreaker on a deadlocked vote — so the working partner must either negotiate from zero leverage or dissolve the company. A ten-page operating agreement specifying a valuation formula, a twelve-month payment schedule and a deadlock procedure would have made it a two-week administrative task.