Molecules absorb specific colors of light when their electrons jump to higher energy levels. The energy of the absorbed light must exactly match the gap between these levels. A bathochromic shift means this internal energy gap has become noticeably smaller.
Because red light has lower energy, the light absorption shifts toward the red end of the spectrum. Several different chemical factors can cause this internal energy gap to shrink. The most common cause is adding more alternating double and single bonds to the molecule.
Chemists call this pattern of alternating bonds an extended conjugated system. When the conjugated system gets longer, the electrons can spread out over a larger area. This spreading out lowers the energy needed to excite the electrons.
Changing the solvent around the molecule can also cause a red shift. For example, moving a molecule from water to oil might alter how its electrons behave. Students often think a red shift means the substance will always look red.
However, the shift just means the absorbed light moves toward the red direction. The actual color you see is the light that the molecule does not absorb.