A buy or sell order made at the best market price. If the order cannot be completely filled, a limit order is placed for the remaining shares at the price at which the filled portion was executed.



Taobiz explains Box-Top Order
For example, if a trader entered a box-top order to buy 1,000 shares at the current market price of $50, and only half of the shares are traded at that price, then a buy limit order is placed for the other 500 shares. If at any point during the life of the order the price returns to $50, the limit order kicks in and the remaining shares will be traded at $50.