Piercing the corporate veil refers to holding liable company directors or shareholders for the actions of a company. Usually, a company is a discreet legal entity, in effect a legal 'person'. In theory, based on this separate legal entity, a company is the responsible party for actions taken in its name. In practice, that apportionment of liabilities doesn't work, nor is it reasonable to assume that a purely hypothetical legal 'person' can commit fraud, etc. Courts can deem a person or persons as responsible parties, rather than the company, for legal issues.
Examples of Piercing the Corporate Veil: