The Sun emits electromagnetic radiation in almost every frequency, from radio to visible light and even some gamma. Some of this radiation is absorbed by Earth's atmosphere and some of it is reflected. About half of the Sun's electromagnetic radiation reaches Earth.
Earth is made of different particles that can absorb the different frequencies of this electromagnetic radiation. Absorbing electromagnetic radiation excites Earth's particles, which causes them to vibrate. Vibration of the particles causes Earth to heat up.
When a particle gets excited, the charge distribution of the particle changes. Eventually, the particle "relaxes", and the charge goes back to normal. This releases energy in the form of electromagnetic radiation. When the particles of the Earth "relax" they release energy in the form of electromagnetic radiation in all directions. This electromagnetic radiation is in the infrared part of the spectrum.
The atmosphere is also made up of particles. Some of the particles absorb the electromagnetic radiation from Earth, and some reflect it in all directions.