Question

Why do molecules vibrate?

Answer 1

Because the lowest temperature we've accomplished for molecules is not quite `"0 K"`. But seriously though, the question doesn't really have a true answer; this is like asking, "why do people breathe?".

Just as people breathe because breathing takes in the oxygen from the surroundings and cyclically incorporates it onto hemoglobin (so that eventually we breathe out `"CO"_2` and breathe in oxygen again later)...

...molecules vibrate because vibrations take in the energy from the surroundings and cyclically incorporate it into constant natural vibrations (again, and again, and again).

If a molecule did not vibrate, there is much less the surroundings can transfer energy into, the human-constructed law of conservation of energy would no longer hold true, and energy from the universe would be in excess.