What crucial function does Earth’s protective magnetosphere, generated by its core, provide regarding habitability?

It deflects harmful charged particles streaming from the Sun, known as the solar wind

Even if a planet is perfectly positioned within the Habitable Zone and possesses all necessary internal processes, it faces the threat of atmospheric erosion caused by the host star. Earth's liquid iron core generates a powerful dynamo, which in turn creates a protective magnetosphere. This magnetic shield extends into space and functions to deflect the continuous barrage of charged particles that emanate from the star, referred to as the solar wind. Without this magnetic defense, the solar wind would slowly but inexorably strip away the planet's atmosphere, leading to the loss of volatiles and eventually sterilizing the surface, making long-term habitability impossible.