Atoms are constantly in motion, even when they appear to be stationary. When they are heated, the atoms vibrate more vigorously. As they collide with other atoms, they transfer some of their energy to those atoms. The atoms that receive this extra energy become excited and begin to emit light.
Other related questions:
Q: Do atoms emit light when heated?
A: Atoms can emit light when heated, but not all atoms will do so. The light emitted by atoms is usually in the form of ultraviolet or visible light, and can be used for things like welding or creating fluorescent light bulbs.
Q: Why does heat give off light?
A: Heat can give off light because when something is heated, it can produce photons, which are particles of light.
Q: What happens to an atom when heated?
A: When an atom is heated, the electrons in the atom become excited and begin to move around more rapidly. This causes the atom to become larger and to emit light.