Definition of 'At-The-Close Order'
An order specifying that a trade is to be executed at the close of the market, or as near to the closing price as possible. An at-the-close order is one in which the broker or exchange is directed to ensure that an order is only filled at that given time of the trading, in most cases coming just prior to the end of trading on a given day.
This would be the opposite of an at-the-open order.
Investopedia explains 'At-The-Close Order'
It's essentially a market order that doesn't get entered until the last minute (or thereabouts) of trading. With this type of order you are not necessarily guaranteed the closing price but usually something very similar, depending on the liquidity in the market and bid-ask for the security in question. Traders who believe that a security or market will move more heavily during the last few minutes of trading will often place such an order in the hopes of having their order filled at a more desirable price.