A type of limit order to buy or sell shares at the market open if the market price meets the limit condition. This type of order is good only for the market opening and does not last for the whole trading day.
Taobiz explains Limit-On-Open Order
A trader who believes that the market open is the best time to sell his or her shares may want to use a limit-on-open order. For example, say the trader holds 1,000 shares in ABC stock and wants to sell at the market open but also wants to guarantee that he or she will receive at least $50 per share. The trader therefore uses a limit-on-open order. If at open the shares trade above $50, the order will be executed, and if they trade below, the order will not be filled and then be canceled.