How can light be both a particle and a wave at the same time?

[Char. Limit]

I feel ashamed at not already knowing this, but...

How can light be a particle and a wave at the same time? What does this particle-wave act like? By that I mean, is a photon a particle vibrating at a wave frequency or is it a sometimes-particle-sometimes-wave structure or something else entirely?

Try not to mock too much for me asking something even a middle-schooler should know.

 

[diazona]

Can I mock you for asking something most college graduates (physics/chemistry majors excepted) can't be expected to understand?

Wave-particle duality is something that takes many people a long time to get used to, because it doesn't correspond with anything we're used to experiencing in nature. Basically, the idea is that sometimes light exhibits wave-like properties and sometimes it exhibits particle-like properties, but we're none the wiser as to what it really is (if such a question is even meaningful). I don't think the vibrating particle idea would suffice, though, because photons are known to do things that no classical particle, vibrating or not, should be capable of.

 

[Integral]

You may want to read post #3 in the https://www.physicsforums.com/showthread.php?t=104715"