Think of methane like a thick woolen blanket draped over the Earth; it lets sunlight in during the day but traps the body heat of the Earth from escaping into the cold night sky.

M-W-C-N: Methane, Water vapor, Carbon dioxide, Nitrous oxide (The 'Major Greenhouse Gases').

Greenhouse gases absorb and emit radiant energy within the thermal infrared range. When solar radiation hits the Earth, the planet re-radiates this energy as longwave thermal infrared radiation. Molecules like $CH_{4}$ possess vibrational modes that capture these specific wavelengths, preventing them from escaping into space and thereby warming the atmosphere through the greenhouse effect.

Always remember that greenhouse gases must be polyatomic molecules ($>2$ atoms) with changing dipole moments to absorb infrared radiation; ignore diatomic gases like $N_{2}$ and $O_{2}$ in this context.