Panic selling is a wide-scale selling of an investment, in order to get out of an investment (with little regard for the price they sell the stocks). The main problem is that investors react simply out of emotion and fear, without evaluating the fundamentals.
Additional meaning of Panic selling:
Almost all market crashes are caused by panic selling. Most major stock exchanges use trading curbs to throttle the panic selling. This allows people to digest any important information regarding why the selling is occurring, and restore the normalcy of the market to some degree.