1966 rocket booster finally breaks free from Earth

In September 2020, astronomers discovered an object initially thought to be an asteroid. It was later identified as a discarded rocket booster from the failed Surveyor 2 mission in the 1960s. After crashing its lunar lander into the moon, the booster floated in space and eventually got trapped in Earth's orbit. The slingshot effect will now send it into the sun's gravitational field.

What phenomenon allowed the booster to be trapped in Earth's gravitational pool again?

Explain the slingshot effect mentioned in the text.