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Can you describe what an "at close order" stands for? In what strategy could it be used?

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Usually backtests for (long-term) strategies are evaluated on a end-of-day basis where you only consider close prices.

If your strategy performs well in these backtests, hopes are that if you use a market-on-close (MOC) order your performance will not diverge too much from the backtest.

The fact that it won't diverge much is important if you keep backtesting the strategy along with the real trading to see regime changes or similar. If you used end-of-day prices for the backtests but some arbitrary intraday market order, you'd have some difficulties to explain deviations between the two.

What it is: MOC orders can be submitted during the day, but they won't be executed until shortly before the market (or more precise the current session) closes.

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Investopedia defines it in the following way:

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.

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