Piercing the corporate veil or lifting the corporate veil is a legal decision to treat the rights or duties of a corporation as the rights or liabilities of its shareholders. Usually a corporation is treated as a separate legal person, which is solely responsible for the debts it incurs and the sole beneficiary of the credit it is owed. Common law countries usually uphold this principle of separate personhood, but in exceptional situations may "pierce" or "lift" the corporate veil.
A simple example would be where a businessman has left his job as a director and has signed a contract to not compete with the company he has just left for a period of time. If he sets up a company which competed with his former company, technically it would be the company and not the person competing. But it is likely a court would say that the new company was just a "sham", a "cover" or some other phrase, and would still allow the old company to sue the man for breach of contract.
Despite the terminology used which makes it appear as though a shareholder's limited liability emanates from the view that a corporation is a separate legal entity, the reality is that the entity status of corporations has almost nothing to do with shareholder limited liability. For example, English law conferred entity status on corporations long before shareholders were afforded limited liability. Similarly, the Revised Uniform Partnership Act confers entity status on partnerships, but also provides that partners are individually liable for all partnership obligations. Therefore, this shareholder limited liability emanates mainly from statute.