EDIT: What follows is a horrid simplification, but I believed it needed for discussion to proceed. Ask questions or ignore, your choice, but mine and am_U's answers don't come from ignorance or some low-brow contentment. The topic is incredibly complex, and what you said in comment doesn't do it justice.
It's like the two-slit experiment, where light is both a particle and a wave... we can demonstrate it, but we don't know why it happens.
Before any other discussion, I'd like to dispel a possible notion where you might think that 'wave' and 'particle' are mutual opposites or choices. You could take photons or electrons from a double-slit experiment and use 'same objects' in Compton scattering a couple meters away, but that's because they measure different aspects of stuff. If you permit a stretched analogy, it's kinda like when an apple can be checked for color or sugar content -- doesn't mean they're suddenly only either color or sugar, but you're measuring different aspects at the time. Different properties, measured by different principles and methods.
What a photon is, is dependent on (and restricted to) the model. It can be modeled like a ball with energy that'll bounce. It can be modeled like a wave that'll reflect. It can be a cloud of probability with properties of a boson. It can be a 4d submanifold that interacts by an exchange of different 4d submanifolds with other 4d submanifolds (or itself). And that's the thing: it will always be a model.
Don't think I'm trying to brush you off, but I want it to be both informed and informative.