To “pierce the corporate veil” means to disregard a business entity’s limited liability and hold some or all of its owners liable for the business’s debts. 

Most incorporated entities have limited liability. Limited liability is conditioned on maintaining the entity as a legal thing distinct from its owners, however. If the owners do not maintain this distinction – most frequently by treating the business as a piggy bank and co-mingling personal and business assets – the entity may lose its limited liability, making the owners personally liable for its debts.