Broadly speaking, the initial impact creates a vast fireball that kills anyone who can see it. The sky becomes filled with gazillions of meteors, a shower of particles that burn up in the atmosphere on their way down. It is as if the sky itself has caught fire. The heat unleashed by this rain of incandescent debris ignites forests and cities, burning them to embers. Then dust from the impact and smoke from the fires girdles the earth, plunging our planet into a so-called impact winter.
Temperatures drop, and there is no light for photosynthesis.
Plants die, animals die. Animals that happen to live underground, where roots and other food sources are not destroyed, have a relatively good chance of survival. During the impact, the comet is blown to smithereens. The heat of the impact also creates nitrogen oxides. The sulfurous stuff and nitrogen oxides make a corrosive acid rain that strips bare any surviving vegetation.