The "feels like" metric is more closely tied to human stress and safety than raw temperature.

In cold weather (wind chill), wind strips away the thin warm layer of air next to your skin, so you lose heat faster. Hence, "feels colder".

In hot weather (heat index), humidity slows sweat evaporation, so your body can't cool itself as effectively. Hence, "feels hotter".

So it's a lot more useful for decision-making (like what to wear, weather it is safe to run/hike, how much water you need, etc.) than the plain temperature.