The legal separation between a business entity and its owners that protects owners from personal liability for business debts.
The corporate veil is the legal concept that a properly formed and maintained LLC or corporation is a separate legal entity from its owners. The veil creates a liability shield: if the business is sued or can't pay its debts, creditors generally cannot go after the personal assets of the owners (savings, home, car). This separation is the primary reason people form entities rather than operating as sole proprietors or general partners.
The veil isn't automatic just because you filed formation documents. You have to maintain it by treating the business as a separate entity: keep business and personal finances completely separate (separate bank accounts, no personal expenses paid from business accounts), follow corporate formalities (hold meetings, maintain records, document major decisions), adequately capitalize the business, and don't use the entity as a personal piggy bank.
Courts will "pierce the corporate veil" — meaning they'll disregard the entity and hold owners personally liable — when the separation isn't real. This is most common in small businesses where the owner treats the business and personal finances as interchangeable. Maintaining the veil isn't complicated, but it does require consistent discipline.