The sentence: “he forgot to pop the flaps to slow down the landing”
What does exactly mean “pop” in this sentence? Could you give me more examples?

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"pop" in this context means to open up quickly, to release quickly. Usually to do something quickly. it almost makes a sort of "pop!" sound because it's so fast and easy.

eg. She forgot to pop the frozen foods into the freezer before running out the door.
eg. "Let me just pop into the supermarket quickly, I need to buy some eggs for dinner."
eg. He popped the sweet into his mouth and waved goodbye.
eg. Let me pop the sun umbrella up before we burn.
eg. Can you pop this CD in so I can listen to Taylor Swift?

In the case of the flaps on the airplane, imagine them "popping up" appearing quickly when the pilot presses the button. A jack-in-a-box would "pop up" .
an ad on your computer would "pop up". Actually, those types of ads are known as "pop-up ads".

A relative you don't like would "pop up" at your house when you're in your pyjamas.